Heart of the TARDIS
The Heart of the TARDIS was a core element of TARDIS technology, described by the Doctor as the ship's "soul." The connection to the Eye of Harmony was unclear. Whether it changed positions like other rooms in the TARDIS was unclear, but for the fifth, ninth, and eleventh Doctors, it was located beneath the central console.
The heart worked to the keep the occupants in time with their surroundings. If it endured problems, such as a skipped beat, the TARDIS would materialise. (ST: 1963)
Commander Maxil removed the heart (or part of it) to stop the Doctor from leaving Gallifrey. Damon reassembled and replaced it. (DW: Arc of Infinity)
When trying to get Vislor Turlough to sabotage the TARDIS, the Black Guardian directed him to the heart of the TARDIS, describing it as a space-time element, and ordering him to rip it out. While he could not remove it completely, he tampered with it enough to cause the TARDIS to begin to break up. (DW: Terminus)
On one occasion, it opened as if by itself because Blon Slitheen had programmed a Tribophysical waveform macro-kinetic extrapolator to tap into the greatest power source available, in this case the TARDIS. (DW: Boom Town) On another occasion it was forcibly opened by Rose Tyler, Jackie Tyler, and Mickey Smith, using an attached chain and the pull of a large, yellow tow truck. (DW: The Parting of the Ways)
The Heart appeared to be bright energy which varied in colour from milky-white to orange. (DW: The Parting of the Ways) Another account stated that the heart of the TARDIS was a glowing blue ball of Zero matter deep inside the structure and was able to neutralise anti-time. (BFA: Zagreus)
The Heart was also said to contain the last traces of Huon particles. (DW: The Runaway Bride)
When Blon Slitheen looked into the Heart she regressed back to a Raxacoricofallapatorian egg, fulfilling her wish for a clean slate. (DW: Boom Town)
When Rose Tyler looked into the Heart it fulfilled her wish to save the Doctor and infused her with the Bad Wolf entity, so she could telepathically operate the TARDIS, sending it to Satellite Five and use god-like powers. In the process she was also infused with vortex energy. To save her life, the Ninth Doctor took the energy into himself at the cost of his own life, regenerating into the Tenth Doctor. (DW: The Parting of the Ways)
Following a highly damaging crash landing, the TARDIS reconstructed itself. Subsequently, the Heart of the TARDIS was relocated to a small sphere beneath the main console, which was itself partially submerged in a blue oily liquid. (DW: The Eleventh Hour)
It seemed that when the Silence took control of the TARDIS to explode it, the explosion started at the heart. (DW: The Pandorica Opens/The Big Bang)
When the TARDIS was lured into the bubble universe, House removed the heart of the TARDIS and stored it in Idris's body to keep it out of the control room. (DW: The Doctor's Wife)