There are many different schools of psi in the Reach, but most of them are restricted to a single planet. The main Reach-wide school of psi is the Quartet or Quadrivial school developed on Earth in the century after psionic physics was introduced. In it, all psychic skills are developments from and combinations of four basic ones: telepathy, clairvoyance, levitation, and dicing. Quartet psi is common heritage for both Old Settlers and New Terraformers.
New Terraformers, however, do not care much for psi. The standard reason is that it takes too much effort for the results, and that the variety of psi talents is too great, and their psychology too quirky, to organize effectively. (Not using an organizational framework does not occur readily to New Terraformers.) These reasons are true to a degree, but the main reason they don't like psi is a distrust of something so powerful that need not coincide with the chain of command. Thus psi in the Reach is driven into Old Settler cultures and other fringe populations. This is especially true in the Empire.
Imperial toleration of psi varies from zero to grudging, varying over time according to the policies of the current Imperator. Even in the most tolerant times, there is widespread propaganda against psi. As toleration diminishes, practicing psies must be registered, then licensed, then latent psies must be registered. Then, no practicing psi can be a government employee, then no latent psi. Finally, it is forbidden everywhere (except, of course, for certain specific tasks called for by the government).
(A "latent psi" is Imperial jargon for someone who exercises a psychic power unconsciously. It is likely that all humans are, in this sense, "latent" to some degree, but in practice "latents" are those who get suspected of being latent, then get tested (by machine) and are found to have a sufficiently high level of psionic residues about them.)
Even during the most psi-intolerant regimes, the Empire finds it convenient to use psychic talent occasionally. Then, they either hire it from outside, draft an illegal psi from within, or – very occasionally – have staunchly loyal "latents" trained, usually by outside experts.
Within or without the Empire, New Terraformer culture has only limited use for the various psychic talents, and has alternatives for all of them:
In the popular media of the New Terraformer cultures, psies as minor characters are often depicted as eccentric, either zany or morbid. Psychic villains are psychopathic, tyrannically self-disciplined, or both. Psychic side-kicks or love-interests, when not comically zany, are haunted, burdened figures. If psi is part of the solution in a plot, then it was also generally the root of the problem, too. New Terraformer governments, such as the Empire, support and reinforce these cultural themes.
Popular impressions of psi vary according to educational level. Well-educated people, especially with any scientific or technical background, differentiate fairly well between psi (real) and magic (mythical), though the exact placement of the border may be vague. Poorly-educated people fail to distinguish and believe in magic/psi freely.
Psi has a disreputable cachet. Young people poke around with it because they have to satisfy childish curiosity. Aliens may use it, but they're icky and alien. Old Settlers and Koliot Raiders and the counter-culture generally "resort" to it because they are losers and lack access to the more reliable alternatives to psi. Spacehands find levitation and other TK very useful, but that's all of a piece with their "mischievous kids" image. To use psi outside some kind of sanitizing framework is at least in questionable taste, using an unfair trick in the game of getting along or progressing in New Terraformer society.
Psi is still interesting to many people, and, of course, may even be more interesting because of its disreputability. The slang terms "path" or "pather" (telepath), "clair" (clairvoyant), and "kick" or "kicker" (telekinetic) are fairly widely understood.
The uneducated do not differentiate the different kinds of psi talent, or distinguish psi from magic. As far as they are concerned, psi is real so magic is real, and fortune tellers or "counsellors" or "wise folk" (or whatever the local hedge wizards are called) are simply "psychic." Being "psychic" in the folk-sense is thought to give a kind of scattershot omniscience, the ability to bless or curse, the power to create charms for various kinds of luck, and a general insight into matters arcane and spiritual.
Among the lower classes and out-groups like Old Settlers, the disreputability of psi does not matter, since they are already disreputable themselves. Or it matters only if you are trying to be upwardly mobile. The lower classes tend to be poorly educated, of course, but not necessarily, and a well-educated Old Settler usually approaches psi with much the same attitude as a native of Terran Space, where psi is common.
psilencers (& mind-screens, TK-blocks, clair-cloaks)
ampsies
telepatches
phase blocks
psi analyzer
thought printer