An Illusionist is a form of Specialist Wizard in Dungeons & Dragons. Practicing the school of Illusion, the magic of altering perceptions and playing upon the mind (which, alongside Enchantment, is one of the schools that most overlaps with psionics), Illusionists are actually the oldest specialist caster in the game - introduced way back in Advanced Dungeons & Dragons 1st edition, they were an entirely separate class to the original Magic User (even once reclassified as a subtype of wizard, they would continue to get arbitrarily special treatment compared to other specialists all the way until 4th edition). This early proto-class traded access to the Magic-User's spell list and to most of the magic items in the game to instead wield its own spell-list full of mind-whammying spells, which were gimmicky but powerful if used right. From this basic concept, the other specialist mages of AD&D 2nd edition were born.
Like Enchantment, Illusion suffers heavily in 3rd edition because practically every other monster in the game is immune to it. They also suffer a stigma of being heavily associated with gnomes; it was literally the only kind of wizard they could be.
Illusion is, in many ways, one of the most "grounded" magical styles, with a strong history in pulpy fantasy stories like Conan the Barbarian.
Illusion is one of the two spell schools most associated with the Arcane Trickster; after all, when you're a rogue, wouldn't you rather drop guaranteed-to-work magical camouflage on yourself rather than trusting the arbitrary efforts of dice?
Illusionists proper vanished in this edition, but the concept survived. Many wizard powers had a theme of being illusions, but illusions lost their "special status" - which was actually a positive thing. Sure, you were doing plain old Psychic damage and not some nebulous "other" damage, but it meant no creature was specifically impervious to your illusion spells, either. No more dealing with some of the most common enemies in the game being immune to your spells. Whilst the PHB had some illusion themed spells, the splatbook Arcane Power really brought the school back to its glory days, with one of the dedicated builds even being called the Illusionist.
That said, illusion spells and enchantment spells did have a bit of overlap in this edition. For example, the most powerful illusion spell in Arcane Power was "Visions of Wrath", which could whammy a whole bunch of enemies and make them start attacking each other.
The Illusionist returned as a subclass for the Mage in Dungeons & Dragons 4th Edition. Being an Illusionist was handled as a set of three features gained by choosing that specific magical school, and which were acquired at levels 1, 5 and 10. A Mage could also dabble in Illusion by taking the 1st and 5th level Illusion school benefits at levels 4 and 8.
- Illusion Apprentice: When you hit a target with an arcane illusion power, the target takes a -2 penalty to the next attack roll it makes against you before the end of your next turn.
- Illusion Expert: You gain a +2 bonus to Bluff checks and Stealth checks.
- Illusion Master: When you hit or miss a target using an arcane illusion power, the target grants combat advantage for the next attack made against it before the end of your next turn.
One huge change to illusion magic in this edition was that, in exchange for the guaranteed effectiveness, it lost its general abstractness. Illusion spells in 4e had defined effects on what they did to their targets, instead of being vaguely phrased "make 'em up" castings like the various Create Image spells of AD&D and 3e. You could still specify just what it was an illusion spell made your victims see, hear or otherwise perceive, but that was mostly flavor text, and trying to create specific spectral imagery was handled through a combination of utility spells like "Illusory Wall" and asking your DM if you could combined with a skill check - for example, an Arcana check to make an illusory bridge to try and dupe enemies into crossing over it.
5th Edition's Arcane Tradition
Illusionists are simple but effective, focusing on super-charging their illusions in various ways. At level 2, thanks to Improved Minor Illusion, not only do they get the Minor Illusion cantrip for free (or a bonus cantrip, if they already knew it), but now they can make both sounds and images in one casting of Minor Illusion. Their level 6 feature, Malleable Illusions, lets them reshape their illusion effects on the fly. Illusory Self, their 10th level feature, gives them the power to force an auto-miss on an enemy attacker once per day by using a reaction to make a one-shot illusory double take the hit for them. Finally, their most potent ability is the level 14 trait of Illusory Reality, which lets them make aspects of their illusions real for a short time. Say, making an illusion of a bridge over a chasm that you and your buddies can run away over, but which will drop anyone else straight through it, Looney Tunes style. Some DMs may actually agree to interpret this ways that're even more powerful, such as using it to create expensive spell components or to defeat enemies by encasing their weapons (or bodies!) in blocks of "faux-real" stone.