Telepathic circuits

Telepathic circuits are a component of TARDISes that allow communication with the Time Lords and other alien races (DW: Frontier in Space, The War Games)

Additionally, this is the element of the TARDIS systems that allows its occupants to understand and speak languages other than their own. The TARDIS's pilot seems to be an integral part of the telepathic circuits; if the Time Lord is unconscious or severely injured, the translation effect may not work correctly. (DW: The Christmas Invasion)

While the Doctor's companions hear and speak their native languages and do not perceive the translation effect, the Doctor himself is aware of the translation and whatever local language is being spoken. (DW: The Fires of Pompeii, The Girl in the Fireplace)

Should someone benefiting from the translation effect attempt to override it and deliberately speak the local language, it comes across to the locals as garbled up. It also seems that the listener (at least in Earth's past, present, and future) hears something similar to the language of the speaker's native culture in that time period. It is also possible that the listener simply hears the native language of the speaker without comprehending it. (DW: The Fires of Pompeii) However it should be noted that the sentence said "Veni, vidi, vici" can also be translated from Slovenian, a language similar to Celtic, meaning the telepathic circuits it might only work on a person's native language.

The translation circuits translate writing as well as speech. (DW: The Fires of Pompeii, A Good Man Goes to War) They do not work on languages that the Time Lords themselves don't know suggesting it acts like a translator with a vast amount of different languages. (DW: Four to Doomsday, The Impossible Planet) The translation circuits are capable of translating all text in an area to show one specific message, such as when the TARDIS translated all text on Shan Shen to "Bad Wolf". (DW: Turn Left)

The telepathic circuits could be used to send messages telepathically to other people. The Third Doctor once used them to send the Time Lords a message about the Master's alliance with the Daleks when both sides attempted to trigger a war between Earth and Draconia. Idris used this function to lead Rory to an archived TARDIS control room, allowing him to drop the shields and allow the Junk TARDIS to enter the Doctor's TARDIS. (DW: Frontier in Space; The Doctor's Wife)

The telepathic circuits can also be used to alter minds in other ways. The Seventh Doctor used his TARDIS' telepathic circuits to erase some of his useless memories, accidentally erasing Ace's memory as well. Shortly afterwards, the Doctor then used the circuits to bring forth the personality of his third incarnation when he had to disarm a cobalt bomb and was uncertain of his present self's technical expertise in handling such a delicate piece of machinery. (NA: Timewyrm: Genesys) When he restored Ace's memories to her, he accidentally gave her some of Melanie Bush's also, allowing her to remember Paradise Towers. (NA: Timewyrm: Revelation) On another occasion, the Doctor was able to transfer his entire conscious mind into the TARDIS telepathic circuits, erasing his own memories while protecting his conscious mind from a telepathic assault that was attempting to provoke him into killing Ace, although this left him an amnesic until he was able to make contact with the circuit again, restoring his memory while using the circuit as a 'barrier' to prevent his enemy attacking him again. (PDA: Matrix)

The Eleventh Doctor demonstrated that the circuits could also pinpoint the saddest memory in the life of the one touching them. (However, if the Doctor used them for such a feat, it could be presumed multiple answers would be given) Even if the memory seemed too ridiculous to be her saddest memory, Amy was encouraged by the Doctor to replace the ice cream she lost in 1994 to make her past self happy. (DW: Good Night)