Well.. as for the Master.. the Childhood history is only coming out with the new series since (Post Dr. Who movie)
In previous episodes under the classic doctors like Jon Pertwee, Tom Baker, Peter Davis, Colin Baker, Sylvester Mccoy, Paul McGann... The Master seems to be a bitter Rival that fell out of grace with the Time Lords by something the Doctor did to bring the evidence to light.. IIRC a plot to overthrow the government of Gallifrey and take control of the Timelords himself.. The Doctor thwarted this plot, the master was exiled / sentenced to death (combined to read as to die in exile never to return to his home world alive, lest the time lords execute him upon his return).. Thus causing the undying need to get revenge on the Doctor.
After all the Doctor was Gallifrey's best and brightest.. though slacked off academically.. he was basically their 'Chosen One' whom was destined to lead Gallifrey (see the 5 Doctors.. The Doctor is suppose to be president but keep running from the post.. Romona (Doctor Who with Tom Baker) eventually becomes the next president of Gallifrey during one of the Time Wars.
The Time war History :
The conflict was between the Time Lords and the Daleks, resulting in their mutual destruction, which the series suggests was caused by the Doctor himself. The Doctor also referred to this conflict as "the last great Time War," implying that there had been others, but it is also implied in various media that all traces of the several earlier Time Wars have been removed from history. Lasting thirty thousand years, it is fought between the Time Lords and other races that are developing time travel. The Time Lords destroy one such race, the Charon, before they even exist. The origins of the Time War dated back to 'Genesis of the Daleks' (1975 - Tom Baker) where the Time Lords send the Fourth Doctor into the past in an attempt to avert the Daleks' creation, or affect their development to make them less aggressive.This war takes place a generation after the time of Rassilon (as in after Rasalon's last regeneration.. as in being utterly dead), the founder of Time Lord society. The Doctor was responsible for destroying both the Dalek fleet and his home planet Gallifrey, after the Dalek Emperor gained control of the Cruciform. It is also stated that the whole of the Time War was "time-locked", so that no time traveler could go back into it, which explains why the Doctor cannot go back in time and undo his destruction of the Time Lords within the war (although Dalek Caan is able to circumvent this, albeit accidentally, and rescue Davros, at the cost of his sanity).
So Rasalon was dead a Generation WHILE Tom Baker was in the past a Generation after Rasalon died.. As such, Rasalon being alive with the Daleks destroyed ships on Gallifrey's surface and the time war going on.. that is the break in continuity.
So now.. not only did the Master get Ressurrected, but it seems that Rassalon got resurrected as well during the last years of the Time War and the Doctor had to destroy both the Time Lords and the Daleks.
Rassilon himself, founder of the Time Lord Society and co-creator of the civilization's time travel technology, returned from the apparent grave to lead his people as the Time Lord President. Rassilon's rule would ultimately see a fundamental change in the war and the Time Lords themselves, as Rassilon's refusal to die or allow the Time Lords civilization he created be destroyed led the Rassilon to prepare a doomsday scenario where he would sacrifice all of time itself; past, present, and future, as part of a genocidal scheme to destroy the Daleks (and all life in the universe) to transform Time Lords into a collective consciousness that would be the only sentient form of life in existence. This mad scheme would ultimately attract the attention of the Doctor himself, who by this point had discovered a way to end the war at the horrific cost of destroying both the Daleks and the Time Lords. By this point, the entire period of war had become "time locked" (meaning no Time Travel was allowed in or out) due to excessive use of temporal warfare, as Rassilon and his council discovered a way to escape the Time Lock as Gallifrey was attacked by its many enemies. In the end, they manipulated the Master by planting a four note drumbeat (the beating of a Time Lord's heart) into his brain and used a White Diamond only found on Gallifrey to create a link between the final hours of the Time War and bring Gallifrey, the Time Lords, and the host of horrors laying seige to the planet, outside the Time Lock and into the present. This plan ultimately failed though as the Doctor destroyed the diamond link, sending Rassilon and the Time Lords back to their apparent doom, with the Master seemingly sacrificing his life (his true fate remains unclear) to ensure Rassilon would not be able to get revenge upon the Doctor.
Got to love the Time War for Continuity errors ...
The Time War also provides a convenient in-story explanation for any contradictions in series continuity: for example, writer Paul Cornell has suggested that Earth's destruction by an expanding sun in "The End of the World" five billion years hence, as opposed to the original depiction of its demise around the year 10,000,000 AD (The Ark, 1966) can be attributed to changes in history due to the War.
Anyhow.. Love the Old series.. the new series is OK.. but they need to slow it down and make it more like the old series where 1 storyline takes 2 -3 or even 6 weeks to complete.. Remember Tom Baker episodes like Legopolis.. 6 parter.. took 6 weeks to see the end of Tom Baker and the beginning of Peter Davis.
Anyhoo.. in this world today.. cram and rush plot lines.. making crappy stories covered with fast pace and action scenes.. wish it was more intellectual like the classic Doctor Who.