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
In 2004, the 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)

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 was able to spread the Bad Wolf meme 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 were capable of reducing a number of 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, using it to conclude 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 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's also shown that even short exposure to the vortex can change a human embryo into a Human/Time Lord hybrid, if they are conceived in the vortex or a vessel travelling through the vortex (ie: the TARDIS). (DW: A Good Man Goes to War)

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 similar light to the Heart of the TARDIS.

Appearance
From inside, the vortex seemed to be a long tunnel that spiraled and twisted off in many directions. It is unknown why the Vortex's appearance changed, though it had done several times. Another possible answer is that there is more than one version of the Time Vortex coexisting and it is the Doctor's (or TARDIS's) prefrence 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 Eleventh Doctor's era, there were were also bolts of lighting which also hit the TARDIS whilst it was travelling through the blue vortex while the red vortex firy. (DW: The Pandorica Opens)

Mechanics
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.
 * The TARDIS seems to spin slower in the Blue Vortex than in the Red Vortex, where it spins as if it is out of control. The TARDIS in the blue vortex is spinning as if in a blueshift where it progress backward through time slowly or at a level speed. The red vortex represents the redshift in which the TARDIS has to be at a certain place in time really quickly as shown in The Lazarus Experiment, the following story 42 and in Utopia.
 * It is unknown if the mysterious time-sequence in the title sequence of the 1960s is meant to be the Vortex or not. When the TARDIS leaves Earth for the first time in An Unearthly Child, the time-sequence graphic is overlaid on the faces of the Doctor and Susan, and seems to indicate that the graphics in the title sequence and the Time Vortex are one and the same.