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For reasons which remain unclear there has thus far been very little information released into the public domain about Ms Iris Wildthyme which does not in some way feature a fellow Gallifreyan - the Time Lord generally known as the Doctor.

Some things however, have been made (un)clearer than others...

Iris' TARDIS

Iris' TARDIS is, she claims, an experimental one, left to die on the mountains of Gallifrey by the Time Lords (Veridgris). It is not dimensionally transcendental, but can be rendered invisible (Plague Herds) and is controlled, not by a console, but by driving using a steering wheel, as with a real bus.

Is Iris a Time Lord?

According to both the third Doctor and Iris herself, she is a Gallifreyan, but not originally a Time Lady, coming as she apparently does from outwith the Time Lord elite (Verdigris), although she claims in Scarlet Empress to have been raised by a House of Aunts in the mountains of Gallifrey. Her Mancunian accent and frequent appearances on Earth do seem to suggest that - like her friend, the Doctor - she has some fondness for that planet.

She has the ability to regenerate which suggests that she must become a Time Lady (or at least gained the Rassilon Imprimatur) at some point - possibly due to her interaction with her TARDIS. The worm factions from The Wormery refer to her as 'Time Lady' (Paul Magrs refers to her as 'Time Lord' in a descriptive passage of "Old Flames").

The Sixth Doctor claims that neither he nor the Time Lords know anything about her - because she has scrubbed all her records, Iris replies. (The Wormery).

Iris is one of the four possible Time Lords to survive of the annihilation of Gallifrey in The Ancestor Cell, although given her ability to hop across Gallifreyan time lines she knows about - and experiences - the Gallifrey-free universe before anyone else. In 'End of the World', the ninth Doctor claims to be the last Time Lord - whether that means Iris was destroyed along with Gallifrey in that timeline remains to be seen.

Travels with a TARDIS - the companions

The Doctor - liar extraordinaire

At various points Iris recounts experiences she has had which seem suspiciously similar to the Doctor's own adventures, causing some commentators to suggest that the Doctor is something of a Walter Mitty character.

Of particular interest are the Doctor's adventures in The Web Planet (the same planet of the Zarbi upon which Iris at one point claims to have first met the Doctor, although she also claims to have first met him duiring the French Revolution); The Visitation (the Doctor claims to have started the Great Fire, whilst Iris says, less grandiously, that she was merely there); and The Three Doctors (in which Omega is banished to a slightly implausible universe of anti-matter, rather than Iris' more prosaic seaside B&B).

In "Seven of Thirteen" - Iris' original version of what the Doctor refers to pompously and self-importantly as The Five Doctors - seven incarnations of Iris combat assorted Mechanoids, Voord, Ice Warriors, Ogrons, Sea Devils, Quarks and Zarbi in the Death Zone before confronting Morbius in the Dark Tower (that the Doctor is, frankly, making his story up is demonstrated by the fact that the well-known and respected Time Lord President Borusa is the evil spider at the centre of the Death Zone in his version).

The Iris Thymeline - Incarnations of Iris

Iris is older than the Doctor and has regenerated several times, although her Beryl Reid persona seems to be a favourite (she stayed in it for almost too long, and regenerated into a very similar shape later on).

Iris as Edith Sitwell ["a very old imperious Iris...a grande-dame glittering in a carapace of ebon pearls" (Bafflement and Devotion)]

Iris Wildthyme could be a descendant of Patience or the Time Scaphe Crew, according to Will B Swift . Her mother abandons her and runs off with an off-worlder and she is raised in a matriarchy with dozens of older 'Aunts' in a Gallifreyan House in the mountains of southern Gallifrey. Iris's favorite Aunt was named Baba. When her Aunts all die and she is left alone she tries and fails to be accepted as a Time Lord and, finding her TARDIS dying in the wilderness, leaves Gallifrey. [Iris first appears in print in Marked for Life where she ends up turned into a baby. Alternative Universe, perhaps?]

Iris with a long white braid
Mentioned by the Doctor as a previous incarnation (from his POV) in Scarlet Empress.

Iris as Shirley Bassey
From Mad Dogs and Englishmen, this is Iris under the name of Brenda Soobie, the 'Scots Caribbean songstress" who sings 'Hey Jude' by the Beatles in 1960 and drives a big red bus. This takes place in the post Ancestor Cell Timeline (PACT) and thus Iris as Brenda is one of only four Time Lords to survive that particular holocaust..

Unseen Iris
An unseen Iris incarnation would fit in either here or prior to the braided Iris and/or the Shirley Bassey Iris.

Iris as Beryl Reid ["with frizzy, lilac hair and a silver cardigan and sensible boots" ("Bafflement and Devotion")]
Iris stays in this incarnation for a very long time (outliving 5 of the Doctor's incarnations) and appears in the short stories "Old Flames", "Entertaining Mr O" and "Being An Extract from the Adventures of Iris Wildthyme on Neptune". She turns up in the novels Verdigris and Scarlet Empress, where she regenerates into...

Iris as Jane Fonda ["holstering her hot pink blaster in her thigh high boots" ("Bafflement and Devotion")]
This incarnation of Iris appears in the short stories "Femme Fatale" (where she describes herself as 'Iris Mark 6'), "Iris Wildthyme and the Spiders from Magrs" and "Cabinet of Changes", and in the novel The Blue Angel. Sarah Jane Smith interviews Iris whilst she is working as UNIT's Scientific Advisor in Interference. At some point she also works for the Ministry of Incursions and Ontological Wonders, according to "Bafflement and Devotion".

Iris as Gracie Fields (but with a drink problem)
This mancunian incarnation appears in Excelis Dawns, The Plague Herds of Excelis and The Wormery. Iris appears to live her life out of synch with Gallifreyan time, possibly as a consequence of living and travelling in an 'experimental' TARDIS.

The final Iris
Highlight the text below to view a fairly major spoiler for one of Iris adventures.
The character Bianca in the Wormery is actually a final incarnation of Iris, in much the same relation to her as the Valeyard was to the Doctor, and the club itself is the remains of Iris' TARDIS.