Sleep

Sleep was, in "every sentient being in the universe", an essential (TV: Sleep No More) periodic state of physiological rest during which the body was not active and the mind was unconscious. Both the human and Gallifreyan species slept with their eyes closed. However, while humans normally required a full night's sleep, Gallifreyans could make do with as little as an hour. (PROSE: The Highlanders, AUDIO: Davros) The Doctor was known to have extra adventures while their companions were asleep. (HOMEVID: Bad Night, Clara and the TARDIS) In emoji, 😴 was the symbol used to denote a sleep state. (TV: Smile)

The transitional state between waking and sleeping was known as Hypnagogia. (AUDIO: The Belly of the Beast)

Humans
Even while having difficulty falling asleep during the night, a human would still experience short periods of non-REM sleep.

A human experiencing nightmares could try to perform the following actions in the sleep to wake up: In addition, Tanya Adeola had a theory that a brain in REM had a certain rhythm and that switching it to the heavy beat of alpha might cause awakening. (PROSE: The Stone House)
 * 1) concentrating, which would shift the brainwaves from theta to gamma and beta;
 * 2) observing things not present in ordinary life, which would alert the brain that it is sleeping;
 * 3) screaming, which would stimulate the amygdala and cause an upsurge of adrenaline, forcing the brain to open the eyes to assess the threat;
 * 4) blinking, which could cause the same action in real life;
 * 5) running.

Although a sleeping individual appeared entirely inactive, some functions of their brain were actually more active than during wakefulness. The high amplitude brain waves known as delta waves were associated with sleep. (TV: Kinda) When sleeping, series of thoughts, images, or emotions known as dreams could occur. (TV: The Time Monster)

During a certain stage of sleep, humans experienced an almost complete paralysis of the body, which prevented them from getting hurt while acting out the movements occurring in their dreams. (PROSE: Dry Pilgrimage)

Sleep occurred naturally, but could also be induced through soporific substances, (TV: The Name of the Doctor) technological augmentation of the delta waves, (TV: Kinda) or hypnosis. (TV: The War Machines)

Jack Harkness once claimed that he doesn't sleep. (TV: Ghost Machine)

Time Lords
Young Time Lords and Gallifreyans, such as Susan, needed more sleep than older Time Lords, but much less than humans. Once they past into their first maturation, they only needed one or two hours a night. (PROSE: The Sorcerer's Apprentice)

Indeed, the Doctor did not require much sleep. (AUDIO: Retail Therapy, World Enough and Time, HOMEVID: Good Night, TV: Knock Knock) Though they did not do so often, (AUDIO: Their Finest Hour) the Doctor did sleep on occasion, (AUDIO: The Unknown, TV: Sleep No More) particularly after regeneration, (TV: Sleep No More; TV: Spearhead from Space, Robot, Castrovalva, Time and the Rani, The Christmas Invasion, Deep Breath, The Woman Who Fell to Earth) a big lunch, (TV: Sleep No More; TV: The Two Doctors) when overheated, (TV: "All Roads Lead to Rome") or when no one was looking, (TV: Sleep No More; AUDIO: The War Valeyard) and the Tenth Doctor did have a bedroom aboard the TARDIS. (COMIC: A Rose by Any Other Name)

The Eighth Doctor claimed only to need a little sleep "every month or seven". (AUDIO: The War Valeyard) The Doctor often expressed that "Sleep is for tortoises", specifically in their third, (PROSE: The Scales of Injustice, Deadly Reunion, AUDIO: The Mists of Time) fourth, (TV: The Talons of Weng-Chiang) fifth (AUDIO: A Requiem for the Doctor), seventh, (AUDIO: Red, PROSE: Timewyrm: Exodus), eighth, (AUDIO: Other Lives) tenth, (PROSE: The Last Dodo) and twelfth incarnations. (TV: Knock Knock) Nevertheless, the Twelfth Doctor thought that sleep was wonderful. (TV: Sleep No More)