Chameleon circuit

The chameleon circuit was the component of a TARDIS which changed its outer plasmic shell to assume a shape which blended in with its surroundings.

Function
Default TARDIS exteriors looked like plain, grey cabinets which opened via a sliding door. (TV: The War Games, The Name of the Doctor)

A TARDIS with a functioning chameleon circuit could appear as almost anything desired. The owner could program the circuit to make it assume a specific shape. If no appearance was specified, the TARDIS automatically chose its own shape. (TV: Logopolis) When a TARDIS materialised in a new location, within the first nanosecond of landing its chameleon circuit analysed the surrounding area, calculated a twelve-dimensional data map of all objects within a thousand-mile radius and then determined which outer shell would best blend in with the environment. According to the Eleventh Doctor, his TARDIS would perform these functions, but then disguise itself as a 1960s era police box anyway. (TV: Meanwhile in the TARDIS)

The Doctor's TARDIS
The chameleon circuit was operational during the First Doctor and his granddaughter Susan Foreman's initial journeys together in the TARDIS after leaving Gallifrey.

For the Doctor and Susan's first trip in the TARDIS, to Earth's Moon in the distant past, it took the form of a tall boulder. On their second trip, to a planet orbiting a blue sun, it assumed the form of a giant mushroom. (AUDIO: The Beginning)

When it materialised in Bridgetown on Quinnis in the fourth universe, the TARDIS assumed the form of a wooden kiosk with red and white awnings. (AUDIO: Quinnis)

On Iwa, it again took the form of a boulder. (PROSE: Frayed)

In Worms, Germany in the 16th century, it disguised itself as a shed. (PROSE: The Price of Conviction)

On other occasions, the TARDIS disguised itself as a Corinthian column and a Christmas tree. (PROSE: The Time Travellers)

The Eleventh Doctor travelled back in time to 1963 and destroyed the TARDIS' chameleon circuit so that the TARDIS would always remain a police box, so that the mental image of the TARDIS would be etched into human culture and history. (COMIC: Hunters of the Burning Stone)

Flaw discovered
After Ian Chesterton and Barbara Wright joined the TARDIS crew, it remained fixed in the shape of a London police box after it departed from I.M. Foreman's yard and rematerialised in Earth's distant past. Neither the Doctor nor Susan could explain why the ship had lost its ability to disguise itself. (TV: An Unearthly Child)

However, the Fourth Doctor appeared to know precisely what caused the fault. As he told Adric, he had "borrowed" the TARDIS while she was in for repairs. He simply took it before the technicians got around to "doing the chameleon conversion" because "there were other pressing reasons at the time". (TV: Logopolis)

The nonchalance of the Fourth Doctor about the malfunctioning circuit was far more typical than the First Doctor's earlier characterisation of it as "most distressing." Although he fleetingly lamented the fact that he never got around to having Romana help him fix it, (TV: Logopolis) the Doctor generally seemed to take it in his stride that the chameleon circuit had failed to function. By the time of his ninth incarnation, for instance, he intimated to Rose Tyler that he simply liked its appearance as a police box. (TV: Boom Town) Other Time Lords who encountered the Doctor's TARDIS seemed not to want to repair it, either. When tried to repair the Doctor's Earth-bound TARDIS, he expressed no particular concern with the fixing the chameleon circuit. (TV: The Claws of Axos). Much later, of the Master took possession of the TARDIS for an extended period of time, but made no effort to fix the chameleon circuit. (TV: The Sound of Drums / Last of the Time Lords)

Despite the chameleon circuit's malfunctioning condition, the TARDIS occasionally still did change details of its outer shell's appearance. Though keeping the general form of a police box, it would change such things as the overall exterior size, shade of blue, window panes, lamp colour, and the text which appeared on the telephone hatch. (TV: The Eleventh Hour et al)

Much later, the Eleventh Doctor expounded on the flaw further to Amy Pond, telling her that the circuit scanned the surroundings upon materialisation, decided on the best disguise, but then always disguised itself as a 1963 police box anyway. (TV: Meanwhile in the TARDIS)

The Eleventh Doctor deliberately sabotaged his TARDIS' own chameleon circuit some time before Ian and Barbara followed Susan back to the TARDIS. It was a necessary sacrifice to defeat a plan concocted by the Prometheans, who wished to alter the ancestral memories of humanity to the days when they worshiped the Sun, reverting the species back to a Stone Age mentality. By implanting the image of the TARDIS into humankind's race memories, it established a multi-generational link for them to remember their advancement, because the Blue Box image would be implanted into the Ancestral Memory of Earth's History. (COMIC: Hunters of the Burning Stone)

Repair attempts
Despite a general lack of enthusiasm for repairing the chameleon circuit, there were nevertheless a few efforts made.

The Fourth Doctor was hoping to repair it in Logopolis by using Block Transfer Computations when interfered with the Logopolitans' calculations. (TV: Logopolis) However, earlier in his fourth incarnation, he had described the idea of his future self repairing the chameleon circuit as "vulgar". (AUDIO: The Light at the End)

Nyssa tried to repair it on her own, without even referencing the TARDIS manual. After double-checking her work and finding it surprisingly sound, the Fifth Doctor chose an overly-ambitious environment for the first test of Nyssa's work. He materialised in one of Earth's oceans, whereupon it turned into a whale - both externally and internally. It became so comfortable in its new form that it seemed to forget that it was a TARDIS at all. Only by transmitting his heartsbeat underwater and reminding it of its link to him was the Doctor able to swim into one of its arteries, undo Nyssa's fixes, and return it to its usual police box shape. (AUDIO: The Deep)

The Sixth Doctor's attempt was temporarily successful. He repaired it for a brief period when he returned to Totter's Lane in 1985, but after a few transformations into shapes that still refused to blend into their surroundings--and, on some occasions, even made it hard to figure out how he was meant to enter his ship in the first place – it reverted to its usual police box form. (TV: Attack of the Cybermen)

During his seventh incarnation, the Doctor temporarily used an alternate version of his TARDIS that he discovered in an alternate universe where his third incarnation was killed by the Silurians and took when his own ship was lost in a tar pit. (PROSE: Blood Heat) He was able to restore the functionality of this ship's chameleon circuit. (PROSE: Conundrum) He later reset it to a police box after the Monk hacked into the circuit and nearly gave away its location by turning it into the Statue of Liberty while it was materialised around Nelson's Column, the Doctor concluding that, while the police box look was old-fashioned, he had come to regard it as very him. (PROSE: No Future)

When Donna Noble briefly had an active Time Lord consciousness, she began to tell the Tenth Doctor how he might be able to repair the circuit, but her brain began to overload before she could complete the instructions. (TV: Journey's End)

The Monk's TARDIS
The Monk's TARDIS appeared as a Saxon sarcophagus in an abandoned English monastery of 1066, (TV: The Time Meddler) a large stone on Tigus and a stone block in Egypt in 2650 BC. (TV: The Daleks' Master Plan)

The First Doctor caused it to appear as a motorcycle, an ornamental coach, a covered wagon, a tank and possibly other forms before impishly setting it as a police box to distract the Daleks. When the Doctor stole the directional unit from the Monk's TARDIS and stranded him on an ice planet, it assumed the form of a block of ice. (TV: The Daleks' Master Plan)

In London in 1976, it assumed the form of a wooden desk, a phone booth, a van, a motorcycle and a filing cabinet. (PROSE: No Future)

In the Abbey of Kells in Ireland in 1006, it once again assumed the form of a sarcophagus. (AUDIO: The Book of Kells)

When the Monk took the Eighth Doctor's companion Tamsin Drew to the planet Halcyon in the 33rd century, his TARDIS assumed the form of a Punch and Judy stall. He told her that it could have taken the form of a tree which would have made it less conspicuous but that would also have made it more difficult to find, given that it had materialised in a forest. (AUDIO: The Resurrection of Mars)

The Master's TARDIS
The TARDIS belonging to the Master took on several different forms during his many encounters with the Doctor. It often adapted to fit a need of the Master or to hide it as a generic object, although he tended to program it to adopt the "default" form of a column when he was materialising in a manner where he didn't care if the Doctor knew where he'd hidden the ship. Also the Master Destroyed His TARDIS.

Others
The Rani's TARDIS took the form of both a cabinet (TV: The Mark of the Rani) and a translucent pyramid (TV: Time and the Rani).

Iris Wildthyme's TARDIS took the shape of a red double decker bus (Number 22 to Putney Common), and at one point, according to Iris, was slightly smaller inside than out. (PROSE: The Scarlet Empress, The Blue Angel, Mad Dogs and Englishmen, Verdigris)

The TARDIS of Professor Chronotis looked like his rooms at St Cedd's College. (HOMEVID: Shada)

The TARDIS stolen by the Twelfth Doctor from Gallifrey and used by Ashildr and Clara Oswald became stuck in the form of an American diner. Ashildr was unable to fix it even with the help of the manual. (TV: Hell Bent)

Nomenclature

 * Though reference was made to the TARDIS' supposed ability to change to match its surroundings in the first Doctor Who story An Unearthly Child, the chameleon circuit itself was not specifically referred to until The Time Meddler, in which it was called a "camouflage unit". The device was not mentioned again until Logopolis, in which it was called the "chameleon circuit," the term to which it has generally been referred ever since.
 * In the TV Movie, the chameleon circuit was referred to in dialogue as the TARDIS' "cloaking device", a term from Star Trek.
 * The first use of the "chameleon" nomenclature must be attributed to Malcolm Hulke, who wrote the Doctor Who radio script "Journey into Time" recorded by Stanmark Productions in June 1966, in which the circuit was called the "Electronic Chameleon System".
 * The choice of name was inspired by the ability of chameleons to change their skin colour, which has been generally thought to be for the purposes of camouflage.

Malfunction

 * The real-world reason for the chameleon circuit's malfunction is thought to be of a far more practical nature than in-universe: the TARDIS was originally intended to blend with its surroundings during the 'historical' episodes, which would have required an expensive redress or replacement of the TARDIS prop for every story. Others have suggested that the constant police box shape was selected to provide something contemporary audiences would instantly recognise in any story settings.