The chameleon circuit enables the outer plasmic shell of a TARDIS to assume any shape, in order to blend in with its surroundings. A TARDIS with a functioning chameleon circuity can appear as almost anything, if its owner desires. The owner can program the circuit to make it assume a specific shape or else the TARDIS itself can decide what form to take.
The Doctor's TARDIS' chameleon circuit
The chameleon circuit of the Doctor's TARDIS, however, has rarely worked properly since the First Doctor made a sudden departure from Totter's Lane, Shoreditch, 1963, and has usually remained in the shape of a London police box. (DW: An Unearthly Child)
The Doctor has occasionally attempted to fix his TARDIS's chameleon circuit. He hoped to repair it in Logopolis by using Block Transfer Computations, but the Master interfered with the Logopolitans' calculations. (DW: Logopolis) He succeeded in repairing it for a brief period when he returned to Totter's Lane in 1986, but it quickly reverted to its usual police box form. (DW: Attack of the Cybermen)
The Doctor once referred to the chameleon circuit as a "cloaking device", possibly for the benefit of the American Grace Holloway, who was probably familiar with Star Trek. The fact that he hesitated slightly before using the term "cloaking device" suggests that he was trying to think of an alternative to "chameleon circuit". (DW: Doctor Who: The TV Movie)
- It has been suggested that when the Doctor "borrowed" his TARDIS from Gallifrey, it was in for repairs, and one of the broken systems was the chameleon circuit. The 'real life' reason for the malfunction is thought to be of a far more practical nature: the Chameleon Circuit was intended to allow the TARDIS to blend with its surroundings during the 'historical' episodes -- which would require an expensive redress of the TARDIS prop for every episode.
The chameleon circuit should make the TARDIS fit in to the natural environment of a specific destination (if it is in Ancient Rome, it would be a Roman statue). Although the TARDIS' chameleon circuit is broken, thus causing it to appear unusual in most environments other than 1950's Britain, it remains unnoticable due to the Perception filter.
Other chameleon circuits
Other TARDISes have displayed the versatility of which a working chameleon circuit is capable.
The Monk's TARDIS appeared as a sarcophagus in an English church of 1066, (DW: The Time Meddler), a large stone on Tigus, and a stone block in Ancient Egypt. The Doctor caused it to appear as an Ionic column, a stage coach, a tree, an igloo, a rocket, and a biplane before impishly setting it as a police box. (DW: The Daleks' Master Plan)
The Master's TARDIS has appeared as a horse box (DW: Terror of the Autons), a computer bank (DW: The Time Monster), a Corinthian column (DW: The Time Monster, Logopolis, Time-Flight), a grandfather clock (DW: The Deadly Assassin, The Keeper of Traken), the calcified Melkur (DW: The Keeper of Traken), a police box (DW: Logopolis), a fireplace (DW: Castrovalva), a Concorde airplane (DW: Time-Flight) and an "iron maiden" (DW: The King's Demons).
The Rani's TARDIS took the form of both a cabinet (DW: The Mark of the Rani) and a translucent pyramid (DW: Time and the Rani).
Iris Wildthyme's TARDIS is in the shape of a red double decker bus (Number 22 to Putney Common), and is (at one point according to Iris) slightly smaller inside than out. (EDA: The Scarlet Empress, The Blue Angel, Mad Dogs and Englishmen, PDA: Verdigris)
Professor Chronotis' TARDIS looked like his rooms at St. Cedd's College. (DW: Shada)