A cravat was a form of clothing worn around the neck, both over and under a shirt.
The First Doctor's ensemble regularly featured a cravat. From his kidnap of Ian Chesterton and Barbara Wright to the end of his life, he wore a dark silk cravat, (TV: An Unearthly Child - The Tenth Planet) briefly swapping it for a gingham one at the start of his travels with Vicki Pallister. (TV: The Rescue, The Web Planet)
The Third Doctor wore a number of cravats throughout his life. Immediately following his regeneration, he adopted a silky black cravat, which he wore for a notable period. (TV: Spearhead from Space - Inferno) He then became sporadic in his adoption of cravats, wearing his original whilst combatting the Sea Devils (TV: The Sea Devils) and during his visit inside a miniscope, (TV: Carnival of Monsters) and adopting new patterned ones on a number of occasions. (TV: The Dæmons, The Mutants, Carnival of Monsters)
The Fourth Doctor wore cravats for a period, initially adopting ones green, (TV: Terror of the Zygons) blue and terracotta in colour, (TV: Planet of Evil, Pyramids of Mars) before settling on a dark red one. (TV: The Android Invasion - The Robots of Death) He also briefly adopted a white silk cravat during his final adventure with Leela, which he retained for the first part of his search for the Key to Time. (TV: The Invasion of Time - The Pirate Planet)
The Sixth Doctor wore a wide variety of cravats, them being a mainstay of his outfit. His first cravat was turquoise with a polka dot pattern, (TV: The Twin Dilemma) which he eventually replaced with a similar cravat in red. (TV: The Mysterious Planet) During his travels with Evelyn Smythe, he briefly returned to wearing a turquoise cravat, this time without polka dots, (WC: Real Time) but soon returned to wearing cravats with such a pattern. After briefly wearing yet another polka dot cravat, this time in purple, (PROSE: The Quantum Archangel) he adopted a yellow cravat with a starfield design. (TV: Terror of the Vervoids) By the time of his regeneration, he had returned to wearing his red cravat. (TV: Time and the Rani)
The Eighth Doctor's cravat. (TV: Doctor Who)
While the Seventh Doctor only briefly adopted a cravat whilst visiting Betrushia, (PROSE: St Anthony's Fire) the Eighth Doctor regularly wore a cravat, first adopting a pale yellow silk cravat shortly after his regeneration. (TV: Doctor Who)
The Ninth Doctor wore a dark cravat in 1912 Southampton, (TV: Rose) while the Twelfth Doctor briefly wore a black cravat whilst travelling onboard the spacefaring Orient Express.(TV: Mummy on the Orient Express)
Sergeant Calder and his clone both wore a cravat that matched the colour of their uniforms. (TV: Resurrection of the Daleks)
Luke Smith wore a cravat while fighting the Qetesh. (TV: Goodbye, Sarah Jane Smith)