Roundel

A roundel, (TV: Terminus) affectionately dubbed "the round things" by the Doctor, (TV: The Day of the Doctor) was a decorative feature in TARDISes used to hide circuitry and other functions.

Roundels were a key standard feature in all TARDISes, (TV: Hell Bent) and a standard design for centuries, so much so that they were a telltale sign for identifying a TARDIS. (AUDIO: The Lifeboat and the Deathboat)

Functionality
At least some of these roundels doubled as access covers to circuitry in the walls. (TV: Terminus, Attack of the Cybermen) Some others were small storage units. (PROSE: Doctor Who in an Exciting Adventure with the Daleks, TV: Castrovalva)

The Doctor's TARDIS
The First Doctor's TARDIS had basic white roundels, circular in shape, indented into the wall. (TV: An Unearthly Child) One wall, however, consisted of white hexagons with roundels implemented on them. (TV: Twice Upon a Time) The Second Doctor inherited this design, (TV: The Power of the Daleks) however, when working for the Celestial Intervention Agency, he was given a TARDIS which had roundels that served as the inner technological functions of the ship. (TV: The Two Doctors)

The Third Doctor originally inherited his predecessors' design (TV: Doctor Who and the Silurians) but later added plastic furnishings to the edges of the roundels. One of them then served the role of the scanner. (TV: Day of the Daleks, The Curse of Peladon, The Time Monster) Later, his TARDIS reverted to its previous design. (TV: The Three Doctors)

The Eighth Doctor's TARDIS had circular cut-outs in the support beams. (TV: Doctor Who)

In the Ninth Doctor's control room, the walls of the TARDIS for a time featured backlit hexagons. (TV: Rose) By the time of the Tenth Doctor, overhead lights were added to the TARDIS' illumination, so the roundels fulfilled a mainly decorative function. (TV: Doomsday)

The first of the Eleventh Doctor's TARDIS console room "desktops" had not so many roundels in the walls, but the theme did continue slightly, and there was a larger circular screen set into the wall near the door. (TV: The Eleventh Hour) Another of his console rooms had blue and red neon circles. (TV: The Snowmen)

When the Tenth Doctor's TARDIS interior glitched because of the War Doctor and the Eleventh Doctor's presence and reverted to the War Doctor's desktop settings, the Eleventh Doctor, despite having forgotten their purpose, happily pointed out the "round things" to his predecessors. The Tenth Doctor voiced his love for the "round things", though he admitted he had no idea what they were when his successor asked. (TV: The Day of the Doctor)

The Twelfth Doctor made a minor redecoration to his TARDIS when he added lit-up roundels to the walls, noting that he used to have a lot of "round things" and feeling partly unsatisfied with the lack of more. (TV: Deep Breath) These roundels reminded the Tenth Doctor for "Dalek bumps", briefly mistaking this version of the TARDIS as belonging to the Master. (COMIC: Four Doctors) The Twelfth Doctor later told Clara Oswald that he wanted more roundels in the TARDIS, saying he was about "new takes on old classics". (COMIC: The Hyperion Empire) He eventually did increase the number of roundels featured in his control room, specifically on the lower floors. (TV: Under the Lake)

At some point, River Song found alcohol stored within the roundels of the Twelfth Doctor's TARDIS and took to drinking some of it whenever using the TARDIS without the Doctor's knowledge, much to his surprise. (TV: The Husbands of River Song) The First Doctor apparently started this, as he kept brandy in a similar location within his own TARDIS, and expressed annoyance at how some of the contents had been drunk by the time of the Twelfth Doctor. (TV: Twice Upon a Time)

The Thirteenth Doctor's TARDIS, similar to her ninth and tenth incarnations', lacked the more conventional roundel. Instead, the walls were made up of many hexagonal sections that contained a cog-like pattern that was reminiscent of roundels. A metal framework, wrapped around the raised platform the control console resided on, also consisted of hexagonal shapes, alongside some blue lights. (TV: The Ghost Monument) Some of these hexagonal cutouts functioned as scanner screens, (TV: Can You Hear Me?) while the blue lights functioned as access to circuitry (TV: The Battle of Ranskoor Av Kolos) and general storage. (TV: Revolution of the Daleks, The Power of the Doctor)

Other references
Roundel was among a succession of words which were uttered by the Sixth Doctor to impede a trio of Carrionites. (AUDIO: The Carrionite Curse)

Behind the scenes

 * Though a common enough word in fandom, roundel is a tough word to find in a televised script. However, it has happened, perhaps most clearly in Terminus, where Turlough, Tegan and the Black Guardian use the word several times at the top of the first episode.
 * A scene recorded for The Awakening part one, but edited out of the finished programme due to the episode overrunning, featured Tegan encountering Kamelion with his hand inserted into a roundel in a corridor, learning more about the TARDIS.