In the plant family flowering plants form a group called Angiosperms. In this group there are lineages:
• Amborellaceae: includes just one shrub that, according to the National Geographic (July 2002) “may be the closest living relative to the first flowering plant”.
• Nymphaeaceae which includes the water lilies.
• Illiciaceae which includes the star anises.
• Magnoliids, which of course includes Magnolias, avocado and black pepper,
• Monocots which with 65,000 species (1/4 of all flowering plants), are recognizable because they have just one seed leaf (single cotyledon). This group includes all grasses (corn, rice, wheat,...), palm trees (which are giant herbs) and flowers such as lilies and orchids. Orchids by themselves account for nearly 25,000 species.
• And, finally, Eudicots (formerly dicots because of their two seed leaves), the largest group of angiosperms with 170,000 species, many of which are woody plants.
Most of this information is from the above mentioned National Geographic issue.
What distinguishes orchids from other flowering plants is the combination of three elements:
• their pollen (called “pollinarium”, plural = pollina) which is formed into a mass (usually 2 masses),
• stamens and pistils are joined together in a structure called a “column”,
• their seeds are very small (there may be up to 3 million in a seed capsule), they do not contain endosperm and have no organized embryo.
Orchid flowers consist of:
• the pedicel (the stem of the flower which includes the ovary),
• the sepals,
• the petals,
• the column.
Sepals and petals are in threes.
The three sepals consist of the dorsal sepal and two lateral sepals.
The three petals consist of two petals and a modified one called the labellum, or more commonly, the lip.
Besides these morphological differences most orchids differ from other plants by the way they grow in nature.
Most orchids are epiphytes, that is they grow attached on other plants (usually trees). They are not parasites, that is they do not take anything away from the plant they grow on, they merely use the other plant (tree) for support.  
Some orchids are lithophytes, that is they grow on rocks.
Some other some are semiterrestrial, that is they grow on the ground, on decomposing plant material (not quite soil).
And finally, a small number of orchids are true terrestrial, meaning they grow in soil like most plants.
Confucius, the Chinese philosopher, grew orchids in the fifth century BC and wrote a poem about them.
Theophrastus, a Greek philosopher and scientist, mentions orchids in his “Essay on Plants” published around 300 BC
Dioscorides, a Greek botanist, physician and pharmacologist mentioned orchids in his work “De Materia Medica” ( “Of Medical Maters”) published around 60 AD This work remained a reference manual till the Middle Age (1,400 - 1,500 AD).
Orchids, in those times, were believed to have medicinal properties, one of them being an aphrodisiac.
And about 2,000 years ago Greeks gave orchids the name “orkhis” which means testicle, because of the form of their pseudobulbs (pseudo = Greek for “false”).
In more recent times, the first record of orchids in cultivation dates back to 1731 in England. Philip Miller mentioned several orchids in his second edition of “Dictionary of Gardening” (1768).
Records of the Kew Royal Botanical Gardens show that Epidendrum cochleatum flowered for the first time in cultivation in 1787. Ten years later 15 orchid species were cultivated at Kew.
Cultivation of orchids started in earnest in the 19th century. At that time orchids were brought to Europe by companies or individuals who financed collecting expeditions. They commissioned professional collectors who traveled for months all over the world in search of showy new species. Like treasure hunters these expensive enterprises were often shrouded in secrecy and it was not unusual for them to spread misleading information about the locations where new orchids were found.
New exotic orchids were most often sold at Protheros & Morris & Stevens Sales Rooms in London, fetching extravagant prices.
At that time very little was known about the cultivation of orchids and their survival rate was dismal.
Through experimentation and by gathering more information on the growing conditions of orchids in their natural habitat, knowledge was slowly being developed and by 1851 B. S. Williams published the first edition of “The Orchid Grower’s Manual”.
By the end of the 19th century there was enough experience and knowledge about the growing conditions of orchids that many orchids survived and bloomed in England’s greenhouses.
Today there is a wealth of knowledge about growing orchids and modern propagation methods have driven prices to affordable levels. Affordable prices, the fascination exercised by their captivating beauty and their diversity has made them increasingly popular houseplants.
The International Code of Botanical Nomenclature (I.C.B.N.) and the International Code of Nomenclature of Cultivated Plants (I.C.N.C.P.) govern the naming of orchids.
The I.C.B.N. has standardized classification of plants and imposed the following endings:
• family
• tribe
• subtribe

: aceae.
: eae.
: inae.

Example: Orchidaceae
Example: Vandeae.
Example: Sarcanthinae.

Below the subtribe are the genera (singular = genus). Examples: Cattleya, Dendrobium, Phalaenopsis, ...
Note: all of the above have their first letter capitalized.
Within the genera are the names identifying individual plants. Example: Phalaenopsis amabilis or Phalaenopsis Ever Spring.
Names of species are not capitalized: Phalaenopsis amabilis designates a species,
i.e. a naturally occurring plant. Names of hybrids (man made crosses) are always capitalized as in Phalaenopsis Ever Spring.
Finally, within a group of individual plants they may be variations which, for example, may be noted Phalaenopsis amabilis var. formosana.
Variety is often abbreviated as “var.” and is usually reserved for species. For hybrids, varieties will be identified by adding to the name one or several words placed in single quotes as in Phalaenopsis Ever Spring ‘Light’.
All new plants (species and hybrids) are registered with the Royal Horticultural Society of London.
The name of orchids is decided by the discover for new species or by the first person who registers a new hybrid.
Until a new hybrid is registered it will be identified by the name of it’s parents, separated by an X. For example: Phalaenopsis amabilis x Phalaenopsis violacea or Phalaenopsis (amabilis x violacea) or Phalaenopsis amabilis x violacea or, in abbreviated form, Phal. amabilis x violacea.
There are several ways to propagate orchids.
Propagation from seed or sexual propagation
Pollen is used to pollinate a flower. When the seed pod matures (which may take several months), the tiny seeds can be sowed.
Not all seed pods will contain seeds as one or the other parent may be sterile.
The encapsulated seeds are in a sterile environment as long as the seed pod is closed. It will eventually crack open at a certain time, in which case the tiny seeds will have to be decontaminated before sowing them.
Most people prefer to work with a “green pod”. That is a seed pod that has matured but is collected before it starts to open.
The seed pot is externally disinfected to kill any germs, spores, contaminants, ... that may be on it’s surface then it is cut open with a disinfected tool (scalpel,...).
Then the seed masses are sown into a flask which contains a nutrient solution (the flask and its contents were previously sterilized in an autoclave). This flask is called a “mother flask”.
This whole operation has to be performed in a sterile environment. Commercial growers will use an apparatus called a laminar flow hood (see page 36 of An Introduction to Orchids South Florida Orchid Society
The nutrients solutions contain minerals, sugars, charcoal, sometimes banana extracts or coconut milk, ... Agar (a substance like gelatin) is added to make the solution more or less solid.
The flask is sealed, marked / labeled and placed in a growth chamber / room where light is relatively limited and temperatures are relatively constant.
After several weeks to several months the tiny seeds will germinate. When they have they will have to be transferred to several other flasks in an operation called “replating”. This is necessary because the mother flask may contain from several hundred to several thousand seeds which now need room to grow.
The replated flask may still contain a hundred to several hundred plantlets, which is way too many plants for the limited space of the flask.
Again after several months the plantlets will be replated and they may need a third replate (some growers replate 4 times !) until they are in their final flask which may contain from 10 to 40 plantlets.
As for the mother flasks, all the replate flasks contain growing media which is different from the germination media. The new replating flasks with their nutrients where sterilized in an autoclave and the flasks to be replated where externally decontaminated. The replating operations are done in the sterile environment of a laminar flow hood.  
Plants resulting from sexual propagation may look like the mother plant or like the father or a combination of both or they may have characteristics of ancestors. In other words they may display very diverse traits.
Among these siblings one or several may be significantly more appealing or different than the others. Whoever possess this plant may recognize its uniqueness by adding a variety name to its name. The variety name is placed in single quotes as in Phal. Ever Spring ‘Light’ or Phal. Ever Spring ‘Cardinal’ or whatever the owner fancies to name the variety. Only that plant and it’s tissue or stem propagated progeny are entitled to bear the variety name.
Tissue culture
As its name suggest tissue culture is done by using plant tissue, mostly the minuscule center of a new growth. A lot of experiments have been made trying to do tissue culture out of leafs, roots,... but so far the most successful method uses tissue from a new growth.
The tissue is excised (cut), its outer layers are removed till the active center of developing cells, the meristem, is reached. Then this tiny mass of cells (it can be less than 1 millimeter in diameter) is cut into 20 or so parts, immersed into a flask with growing solution without agar, so the solution stays liquid. This media for this solution is usually called “multiplication” formula.
The flasks or tubes are placed on an agitator (an apparatus than either slowly rotates or tilts to the left then to the right.  The constant movement of the agitator allows the lumps of cells to develop and increase in mass but prevents them from forming roots or leaves.
Once the lumps have sufficiently increased in size they are further cut into small lumps, placed into flasks or tubes and on the agitator. In this process the original 20 tiny masses may now be 400. At the next subdivision we may have 8,000.
This process continues until the desired number of lumps has been achieved.
Then the developed lumps are replated into flasks as is done for germinated seeds. From there on the process is the same as for seeds.
As in seed propagation all these operations require external disinfecting, and working in sterile conditions.
Plants developed from tissue culture, are called mericlones. They usually are very close in appearance (plant and flowers) to the plant from which the original tissue was taken and they are entitled to be recognized by the same variety name as the plant from which the original tissue was excised. So when you see a plant with a name like Cattleya Irene Finney “Z” it means this plant was propagated through tissue culture, using tissue from Cattleya Irene Finney ‘Z’.
Stem propagation.
In this technique a flower stem is used for propagation. If we propagated Phalaenopsis in this manner we would be looking for a flower stem with just the first flower open or with up to half the flowers open.
Flower buds nearer the base of the flower stem open first. Below them there will be a number of undeveloped buds, which we usually refer to as “nodes”.
The flower stem is removed from the plant and is externally decontaminated.
The stem is cut about 1 inch above and below the node, then dipped in decontamination solution for 15 to 20 minutes.
Then the protective sheath over the node is removed and about 1/8 of an inch is further removed from both ends of the stem (above and below the node).
The cutting is inserted in the media solution which is in a tube or jar or flask which was previously sterilized through autoclaving.
If the operation is successful we may get up to 4 plantlets per node.
Obviously this technique only produces a few plants from a flower stem of the original plant. We may get 10 to 15 stem propagated plants as opposed to the thousands we may get through tissue culture.
Because of the limited yield and the labor intensive procedure stem propagated plants tend to be much more expensive than plants propagated through seed or tissue culture.
On the other hand, unless some abhorrent mutation occurs, these plants will be exactly like the plant they were propagated from.
These plants too are entitled to be recognized by the same variety name as the original plant from which the original tissue was excised.
As with seed propagation and tissue culture all these operations must be conducted in a sterile environment.
Internode propagation
This technique is similar to the stem propagation but instead of using a flower stem as the start up point we use a growth. It is often used with Dendrobiums.
A growth is removed from the plant and is cut in between nodes. The edges are dipped in a fungicide and then either inserted or laid on sphagnum moss kept moist.
If the operation is successful we may get 1plantlet per node, but usually much less than that as many nodes will not develop a plantlet.
Still the technique does not require any sophisticated equipment, is inexpensive and can be done practically by anyone.
These plants too are entitled to be recognized by the same variety name as the original plant from which the growth was removed.  
Divisions & back bulbs
Some orchids grow by developing new growth from the base of the plant. After several years they may have 5, 6, 10 or more growths. We may subdivide such plants to get two or three out of the original one.
Often the older growth or old pseudobulbs of these plants do not do anything but if we remove them and plant them separately they will generate new growth.
Again as for the previous methods where plants were propagated by using tissue, or the fower tem, plants resulting from divisions and backbulbs are also entitled to be recognized by the same variety name as the original plant from which the growth or back bulbs were removed. The resulting plants will be identical to the plant we divided or from which we removed the pseudobulb(s).
Some orchids, mostly Dendrobiums, are notorious for producing keikis which is the Hawaiian word for “babies”.
Occasionally Phalaenopsis will also produce keikis. Some, usually species, do it because it is programmed into their genes, others do it when they are exposed to high temperatures while they are developing a flower stem.
Keikis will develop leaves first. Eventually they will develop roots. When roots have reached about an inch in length we can remove the keiki from the mother plant and plant it in its own container.  
Keikis will be identical to the plant they were removed from and are also entitled to be recognized by the same variety name, if any, as the plant from which they originated.
Top cuts
Finally, some plants, mostly vandaceous orchids, tend to grow very tall. Heights of 4, 5, 6 feet or more are not unusual, making them difficult to handle. These also tend to develop new roots along their stem, in between leaves. These can be divided by
cutting off the top portion of the plant as long as this top portion has at least 2 pairs or roots attached to it.
The remaining (bottom) part of the plant will often respond to this attack by sending out new shoots from its base.
Top cuts are of course the same as the plant they were removed from and are also entitled to be recognized by the same variety name, if any, as the plant from which they originated.