Time Vortex

The Time Vortex, also simply known as The Vortex, was the "place" through which all Time travellers passed. Space-time machines were able to pass through the vortex, including TARDISes and vortex manipulators.

History
The Vortex was built by the Time Lords as a transdimensional Spiral that connected all points in space and time. (NA: Just War)

In 2004, the Eighth Doctor used the power of the vortex to destroy a group of Cybermen from the future and set time back on its proper course. (DWM: The Flood)

The Korven Space-Time Manipulator used a vortex to transport objects and people through time. In 2050, a mysterious phenomenon involving a white hole and a black hole moving together nearly resulted in Earth being sucked into that vortex. Presumably, the vortex in question was the time vortex. (K9TV: The Eclipse of the Korven)

Inhabitants
Native life in the time vortex included the Reapers (DW: Father's Day) and the Chronovores. (DW: The Time Monster)

The Bad Wolf entity also seemed to be linked to the time vortex. When Rose Tyler became the Bad Wolf, she was infused with the time vortex, and the entity spread the Bad Wolf name through time and space, look at all of space and time, destroy the Dalek fleet and resurrect Jack Harkness. (DW: The Parting of the Ways)

Travelling through the vortex without a capsule of some kind could prove harmful to humans and Gallifreyans alike. (DW: Utopia / The Sound of Drums) The energies in the vortex reduced cirque posters attached to the Doctor's TARDIS to burnt cinders. (DW: Vincent and the Doctor)

Energy
Mrs Wormwood detected artron energy in a body scan of Sarah Jane Smith and concluded that she had travelled in the Vortex. (SJA: Invasion of the Bane)

The Cybermen once trapped a section of the time vortex to power their ship. (DWM: The Flood)

When Rose Tyler became the Bad Wolf, she and the Ninth Doctor absorbed vortex energy into their bodies. Rose looked into the Heart of the TARDIS to obtain it, then the Doctor absorbed it from Rose. In both cases, the energy, which resembled bright white-gold wispy light, threatened to destroy their cellular structure, much like radiation. The Doctor had to regenerate in order to survive. (DW: The Parting of the Ways, DW: Children in Need Special)

According to the Doctor, Time Lords evolved and seemingly gained their abilities from prolonged exposure to the vortex over 'billions of years'. It has also been suggested that even short exposure to the vortex could change a human embryo into a human/Time Lord hybrid, were they conceived in the vortex or a vessel travelling through the vortex (ie: the TARDIS). (DW: A Good Man Goes to War)

The physics of the Time Vortex do not operate as realspace, as it is e=mc^3 (DW: The Tardis Handbook)

The Eye of Harmony
All TARDISes had a direct link to the vortex through the Eye of Harmony. (DW: Doctor Who) The Eye gave off a light similar to the Heart of the TARDIS.

Appearance
The Vortex's appearance has changed several times, though this is unknown. From inside, it seemed to be a long tunnel that spiralled and twisted off in many directions. A possible answer to a changing Vortex is that there is more than one version of the Time Vortex coexisting and it is the Doctor's (or TARDIS's) preference as to which one to use. (DW: Utopia, The Pandorica Opens)

The Vortex generally had two different colours, red and blue. Red generally indicated forward time travel and blue indicated travel to the past. During the Fifth and Sixth Doctor's eras, the Vortex was shown on the TARDIS console's as a series of boxes moving recursively.

Whilst being chased by the Daleks, both the Doctor's TARDIS and the Dalek time machine travelled through the Vortex, which had a grey, kaelidoscopic appearance. (DW: The Chase)

After a time ram, both the Doctor and the Master's TARDIS were transported to a greenish-yellow void by Kronos, explained as a place between the universe and Kronos' realm, which may have been the Vortex or the Six-Fold-Realm, as the Vortex was a checkered, green-black spiral at this time(DW: The Time Monster) and the Black Guardian contacted Turlough in a similar green-black place. (DW: Mawdryn Undead).

In the time of the Ninth and Tenth Doctor, the Vortex was a sort of tunnel of blues and purples or reds and oranges. The tunnel was not like the Eleventh Doctor's in the way that it had sort of a transparent look as if it is infinite in all directions.

During the Eleventh Doctor's era, the vortex has looked like a gaseous cloudy tunnel of bluish-grey or burnt orange. There were were also (what looked like) bolts of lighting which hit the TARDIS whilst it was travelling through the blue vortex. (DW: The Pandorica Opens)

Mechanics
The Time Spiral existed at the perimeter of the Vortex. (MA: The Well-Mannered War) Another Spiral, if not the same one, was said to exist at the nexus of the Vortex. (PDA: Spiral Scratch)

The Master explained that E = mc3 in the Time Vortex, as opposed to E equalling mc2 in the main universe. (DW: The Time Monster)

The Doctor mentioned being on the edge of "a time-space vortex," describing the difficulty in navigating a vortex in response to Sarah Jane Smith asking why it took so long to get to London. (DW: Planet of Evil)

Travelling backwards in time in the vortex was akin to travelling "up-hill" and required more energy than travelling to the future. (EDA: Anachrophobia)

Behind the scenes

 * The same Time Vortex was seen in the opening and closing credits from Series 1 to the 2009 Specials (officially part of Series 4). The opening credits and closing credits for Series 5 onwards used another version of the Vortex.
 * Before the broadcast of The Eleventh Hour, promo pictures and a trailer showed the Doctor and Amy falling through a blue, fluid-like vortex. Some people presumed this was the new vortex. When The Eleventh Hour broadcast, the new opening titles showed another vortex, which was a gaseous version of the old vortex.
 * It's a convention of several eras of Doctor Who storytelling that, when the time vortex is shown, it resembles the imagery seen in the opening title sequence. This tradition began with the very first episode, "An Unearthly Child", which used the title sequence imagery within the narrative of the episode. Likewise, the season 6 titles were used to illustrate the vortex seen in DWM: Land of the Blind; the Eighth Doctor's title vortex was seen at several points in the narrative of the 1996 tele-movie; the RTD vortex was used frequently in-narrative, as in DW: 42; and the Moffat vortex was seen in DW: The Pandorica Opens.