Translation circuit

A translation circuit was a part of the Doctor's TARDIS that allowed for the instantaneous translation of most languages spoken or written in the universe.

Basic functionality
As the Doctor once told Rose Tyler, the translation circuit was a "gift of the TARDIS, a telepathic field that gets inside your brain — translates." (DW: The End of the World). The Doctor himself was a part of the circuit, without whom the circuit was broken. When he was incapacitated due to post-regenerative crisis, for example, Rose lost access to the circuit, and could no longer understand languages she did not personally know. (DW: The Christmas Invasion).

Exactly who could take advantage of the circuit, and under what circumstances, was variable, suggesting the Doctor could change its settings in some way. The Doctor told Sarah Jane in Renaissance Italy that it was a "gift of the Time Lord" that he allowed her to share. (DW: The Masque of Mandragora) During the incident with the Sycorax on Christmas 2006, the translation circuit worked for all humans on the Sycorax ship, even though he was not, at the time, apparently aware of their presence. (DW: The Christmas Invasion). On yet another occasion, the Doctor told Elizabeth Klein that the telepathic field was limited to a certain radius around the TARDIS. (BFA: Survival of the Fittest)

Companions
When the Doctor and Donna arrived in Pompeii, Donna wondered what would happen if she spoke Latin to the locals, whose native language was Latin. Instead of hearing Latin, at least one native speaker of Latin believed her to be Celtic. The Doctor then surmised that speaking Latin to a Latin speaker while using the translation circuit resulted in apparent Welsh. (DW: The Fires of Pompeii)

Most of the Doctor's companions were native speakers of English, and the Doctor himself was a "master of English" — indeed a fan of the language. (DW: ...ish) However, he did occasionally travel with non-English-speakers. Elizabeth Klein, a native German speaker required the circuit just to communicate with the Doctor. It made her perceive the Doctor as having a "stuffy Prussian accent". (BFA: Survival of the Fittest)

The Doctor
The Doctor's use of the circuit as a comprehension tool was not well understood. There were times, for instance, when he was able to interject French words into his otherwise English speech — such as one incarnation's wide use of the phrase "Allons-y!" — without the circuit translating the phrase. The phrase was sometimes untranslated even when the recipient was not likely a native speaker of English, in which the phrase was an arguable loan word. (DW: Midnight, Voyage of the Damned, The End of Time)

On other occasions, he seemed able to detect extremely subtle variations in a language, such as when he used Madame de Pompadour's accent to identify the century in which she lived. (DW: The Girl in the Fireplace)

Untranslatable languages
Although the circuit could translate a vast array of languages in the universe, it was occasionally stumped. If a language was one of which the Time Lords had no knowledge, as a language from the Dark Times present on Krop Tor once encountered by the Doctor and Rose Tyler, the translation circuit failed. (DW: The Impossible Planet)

The circuit may also have been unable to translate the native language of the Judoon, as the Doctor appeared to actually speak the language, rather than having it translated. (DW]: [[The Stolen Earth)
 * ''This case is ambiguous, however, and many alternative explanations present themselves. The Doctor may have merely been observing a law of the Shadow Proclamation, trying to curry favour with the so-called "galactic police", or may have deliberately switched off the circuit for a moment so as to conceal his words from Donna.