as far as i am aware there never seems to be any sort of explanation. and it need not be some long drawn out thing, like for example the fact he is a she now could simply be referenced that The Master 'stole' a females body, much like he stole a body in the TV Movie - in which he got sucked into the eye of harmony - how did he get out ?!

How did he turn into derek jacobi then regenerate into john simm when he has run out of lives.

He also stole a body when he returned in the 1980s. Anthony Ainley originally played Nyssa's dad and then the Master took over his body.

Pre-Utopia, the Master was a bit of a mess, to be honest.

He had burnt through his own regenerative life cycle in record time and so when he re-appeared as a horrible smoldering mess in "The Deadly Assassin" it was explained that he had used all 12 regenerations and was stuck as he was.

In "The Keeper of Traken" I believe it was explained that he used power he stole from the Keeper in order to steal Tremas' body. At least, that's how it looked on screen. Who's to say he used the Keeper's energy and Tremas' body to enact a further, one-off regeneration? But, again, he had no power of regeneration after that so could be killed at any time.

The Time Lords offered him a complete new regenerative life cycle if he helped them out in "The Five Doctors" which was the first time it was stated on screen that this could be done. But he didn't get it.

And then we saw him exterminated into ashes in "Doctor Who: The Movie" but use some sort of weird power (left over from the Keeper?) to turn his own remains into a liquid snake form and possess an earth human. And he met a nasty end at the end of that movie too.

So at some point between then and Utopia he appears to have been physically restored AND given the power to regenerate again. I always thought it was a standard offer from the Time Lords High Council - "fight in our time war and you get a brand new regeneration cycle". But then there was all that nasty stuff with him dying and being cremated and being brought back through that ring and so on.

I guess the question for me is really this: how much of the Master is actually left? Its a but like that old question about a broom - you have the same broom for 20 years, but over that time you replace the head half a dozen times and the handle twice. So at what point does it become a completely different broom?

That one was explained.

The Time Lords resurrected him (seemingly complete with new life cycle) to fight in the Time War.

Could probably be said about the doctor as well really. But I see your point. Maybe it's easier to see 'the master' more as a title than a person. Makes ones imagination easier to stretch.

I heard he has a secret stash of clone bodies, ready and waiting to be warmed up and inhabited at a moment's notice...

I don't get why we need to know.

She's a villain. Villains have a tendency to keep coming back beyond death in Good VS Evil storylines. We don't need a explanation.

I used to love the 'explanations' in the 1980s.
We see the Master trapped in Castrovalva. He turns up again in Time Flight and the Doctor says "So you did escape from Castrovalva".
At the end of Time Flight he's trapped again but when he next appears the Doctor says "So you did escape from Xeriphas!" And that's all we need to know.
As Dalekbuster rightly says - s/he is a supervillain and they Always come back. Job done.

He got resurrected in TEOT but it went wrong. He later "died" fighting the other time lords getting trapped. Yet after some how escaping and another regeneration which was also a gender change Missy blamed the Doctor saying he left her for dead !. Maybe some of it will be explained when she returns in the magician's apprentice.

I'm curious now, cos it's not explicitly clear - I wonder if Missy is Simm having stolen a body (akin to the Master taking Tremas' body), or whether Missy is the result of an actual regeneration from Simm. Cos when we last saw Simm, he was presented as being effectively dying and we don't know if he had any more regenerations or not left in him.

Either explanation would be a mistake IMO because it would be pointlessly trying to justify/explain why the Master is now female and we already have a explanation for that (the one presented in The Doctor's Wife).

He was also heading back to Gallifrey with the High Council. Yes, it was slap bang in the middle of the Time War but plenty of opportunity for him to steal the power for even more regenerations. Or, possibly, the body of a fellow (female) Time Lord.

We may never know! But unless it's stated explicitly on screen that he stole another body, I'm going to assume it is his own body and he regenerated into female form.

Well it's gotta be one of the two anyway.

True. I quite like how it's ambiguous. I guess we're meant to assume Simm regenerated into Gomez, but the option is also there to imagine he got desperate and stole a random body too.

Oh god, if that is the case I HOPE it is random. I'd hate it to be the start of complicated story arc