They have been used for thousands of years in native societies and are used today for research and therapy, perhaps some military applications (military research has been done in the 1950s and '60s), but most commonly for recreational use.
They can be classified by quality of action, mechanisms of action or simply by chemical structure. These classifications correlate to a quite high extent, of course. I have combined all of them here to make classes as clear and easy to grasp as possible.
A classical classification is that of Lewin (Phantastica, 1928): Class I Phantastica roughly correspond to the psychedelics, which is a more modern term usually used as synonym to "hallucinogen" by people with positive attitudes towards them. I am using the term here a bit differently to discriminate one particular class of hallucinogens which it seems to describe best. They typically have no sedative effects and there is usually a clearcut memory to their effects. Class II Phantastica correspond to the other classes in this scheme. They tend to sedate in addition to their hallucinogenic properties and there often is an impaired memory trace after the effects wear off.
Psychedelics (Class I after Lewin):
Delirants (Class II after Lewin):