A delusion was a psychological disorder that displayed a false belief that was not necessarily visible to the believer (unlike a hallucination), often brought on by mental illness or trauma.
One of the symptoms of transporter psychosis was paranoid delusions. (TNG: "Realm Of Fear") Excess stress as well as exposure to disulfides could lead to delusions. (VOY: "Persistence of Vision", "Friendship One") According to Data, believing oneself to be perfect is a sign of a delusional mind. (Star Trek: First Contact)
In 2151, the Enterprise NX-01 visited a planet with trees the pollen of which induced hallucinations and delusions. (ENT: "Strange New World")
In 2152, while visiting an unknown planet, Captain Jonathan Archer attempted to convince a general named Gosis he was delusional for thinking there was a spaceship in orbit while trying to conceal that there was a spaceship in orbit. (ENT: "The Communicator")
In 2153, the Enterprise NX-01 encountered the Vulcan ship Seleya. Captain Archer's logs recorded the crew was in a delusional, violent state due to trellium infection. (ENT: "Impulse", "Home")
In 2154, while the Enterprise NX-01 traversed a trans-dimensional disturbance, Doctor Phlox experienced a variety of hallucinations and delusions, one of which resulted in his nearly killing Captain Archer's dog. He recorded his experiences, large sections of which turned out to be fictitious, in a letter to Doctor Lucas, ultimately deciding to preserve the delusional account for the entertainment value. (ENT: "Doctor's Orders")
Also that year, Captain Archer assured T'Pol he was not delusional when he was possessed by Surak's katra. (ENT: "Kir'Shara")
In December of that year, Doctor Phlox discovered the Orion pheromone caused Human males to become aggressive to the point of delusion, and vulnerable to suggestion. ENT: "Bound")
In 2155 of the Mirror universe, T'Pol declared Jonathan Archer delusional based on a speech he gave. Phlox argued it wasn't a delusion if he had the power to carry through with his threats. (ENT: "In a Mirror, Darkly, Part II")
In 2256, when Michael Burnham returned to the USS Shenzhou from investigating a debris field to report seeing Klingons in a structure there, she insisted she was not delusional due to her grade-three concussion. (DIS: "The Vulcan Hello")
In 2257 in the mirror universe, Philippa Georgiou declared equity, freedom, and cooperation delusions and destructive ideals that fuel rebellions. (DIS: "Vaulting Ambition")
Later that year, when Ensign Sylvia Tilly saw May Ahearn on the USS Discovery, she believed she was delusional, as Ahearn had died in 2252. (DIS: "Point of Light")
In 2258 of the alternate reality, Doctor Leonard McCoy referred to James T. Kirk as being delusional due to a Melvaran mud flea vaccine and took responsibility for his condition. (Star Trek)
In 2266, Doctor Leonard McCoy, with the rest of the crew of the USS Enterprise investigated the illness of a director of the Tantalus Penal Colony, Simon Van Gelder. He suffered from neuro-synapse damage, and was possibly experiencing delusions, though McCoy was unsure. He would later request Lieutenant Spock perform a mind meld on Van Gelder to determine if he was having delusions. (TOS: "Dagger of the Mind")
In 2268, Korax accused James T. Kirk of having "delusions of godhood." (TOS: "The Trouble with Tribbles")
In 2269, while Kirk was trapped in Janice Lester's body, Doctor Arthur Coleman diagnosed Lester with the delusion of being Captain Kirk. (TOS: "Turnabout Intruder")
In 2364, when the USS Enterprise-D was investigating the fate of the SS Tsiolkovsky, Captain Picard asked Doctor Crusher to provide a theory as to what happened to the crew. Crusher agreed it could have been madness, mass hysteria, delusion, or all three. (TNG: "The Naked Now")
Later that year, Rear Admiral Savar agreed with his colleague Vice Admiral Aaron regarding conspiracies that when they are real no one knows, when it is suspected it is almost never real, except in paranoid delusions for those who believe them. (TNG: "Conspiracy")
In 2365, when asked what death was, Captain Picard offered several perspectives, one of which was the belief that, upon "blinking into nothingness," all an individual's experiences, hopes, and dreams would be as a delusion. (TNG: "Where Silence Has Lease")
In 2367, while trapped in a warp bubble, Doctor Crusher told a parallel universe version of Captain Picard that her concerns about the crew disappearing was not a delusion or a dream. (TNG: "Remember Me")
Later that year, a Tilonian named Syrus attempted to extract strategic information from Commander Riker by convincing him his life on the USS Enterprise-D was a delusion. He would explain some of Riker's confusion as projecting elements from delusions onto events that occurred in reality, or "transposition." (TNG: "Frame of Mind")
In 2371 of the mirror universe, Jadzia Dax described Terran rebels as "ex-slaves with delusions of grandeur", expressing the futility of continuing to fight against the Terran Empire. (DS9: "Through the Looking Glass")
In 2372, Captain Janeway began experiencing delusions while participating in a holo-novel, which The Doctor theorized could be due to excess stress. Later, the delusions spread to the rest of the crew. Torres believed it was due to a bioelectric energy field modulating on a delta wave frequency with psionic properties. Kes was resistant to the effect. (VOY: "Persistence of Vision")
In 2373, Captain Janeway ingested a Nechani psychoactive drug which had an hallucinogenic effect. Tuvok questioned whether that made her delusional. (VOY: "Sacred Ground")
In 2374, Chakotay tried to convince The Doctor that he was malfunctioning and experiencing delusions due to continuous operation. Later, The Doctor would characterize the experience as an elaborate delusion on the esoteric dilemma of the nature of his existence: whether he was a human or a hologram, person or projection. (VOY: "Projections") Later in 2374, another Emergency Medical Hologram would attribute his more adventurous personality to delusion from continuous operation for four years. (VOY: "Message in a Bottle")
Later in an alternate reality of that same year, Lieutenant Lasca offered the possibility that Ensign Harry Kim could be delusional, or have altered memories, or be an alien masquerading as Kim to explain his erratic behavior. (VOY: "Non Sequitur")
Also that year, Jake Sisko, during an argument while being held by Red Squad on the USS Valiant, sarcastically told Nog that all he cared about was himself and whether delusional fanatics were going to get him killed. (DS9: "Valiant")
Later the same year, Seven of Nine accused a weapons merchant named Kovin of assaulting her. Kovin said she was experiencing delusions. (VOY: "Retrospect")
In 2375, Commander Chakotay appeared to experience delusions when aliens in chaotic space contacted him. (VOY: "The Fight")
When The Doctor's ethical subroutines were deleted later that year, Seven of Nine told him he was delusional. (VOY: "Equinox, Part II")
In 2376, the USS Voyager encountered a synaptic transmitter that caused the crew to experience memories of a past tragedy. Janeway characterized them as delusions. (VOY: "Memorial")
In an alternate version of 2379, The Doctor informed Kes that delusions may be a symptom of the morilogium. (VOY: "Before and After")
In a possible version of approximately 2395, Jean-Luc Picard accused Geordi La Forge of thinking he was senile and experiencing delusions of visiting a USS Enterprise-D of the past. (TNG: "All Good Things...")
In 2399, Fleet Admiral Kirsten Clancy denied Jean-Luc Picard's request to be reinstated for a single mission and called his concerns about the creation of a new organic synthetic pitiable delusions. (PIC: "Maps and Legends")
In an alternate timeline of 2401 created by Q, Agnes Jurati told Spot 73 she felt she could come up with a better delusion than that she was in a "mirror universe" wherein the only difference was an improvement in her pet-programming skills. (PIC: "Penance")
As a Figure of Speech[]
Someone being delusional or deluded sometimes had the meaning of deceiving oneself rather than speculating on a medical diagnosis.
In 2369, when Odo told Quark he was deluding himself for believing Jadzia Dax was infatuated with him, Quark pointed out there was nothing wrong with a good delusion and that he sold them to dozens of customers via holosuites every day. (DS9: "The Passenger")
When Overlookers attempted to extort the USS Voyager in 2378, one of them suggested that they let Captain Janeway go free. His companion asked if he was delusional. (VOY: "Renaissance Man")