The Master returned as a primary nemesis for The Doctor in the revival of Doctor Who. So far, he appeared in three episodes of Series 3, and returned for the climatic special "The End of Time". Whether he survived that episode is not clear, but given the long run of the character on Doctor Who, it is likely that he will return at some point.
In the narrative established in the story, The Master fled from the cataclysmic conflict known as The Last Great Time War, hiding himself at the limits of time, in the year 100 Trillion. He physically and mentally gives himself the identity of "Professor Yana" (played by Derek Jacobi), a kind and intelligent man, and forgets that he is The Master. It is only when The Tenth Doctor visits that he comes back to his senses, and after being killed, regenerates as a younger looking man, played by John Simm. He then attempts acts of megalomania and tyranny that are ingenious and devious, but are still thwarted by The Doctor.
I wish I was more conversant with Classic Doctor Who, but while the Master has always been a genius and a schemer, the latest regeneration of The Master is also insane, although just as intelligent as ever. His tyranny breaks into sadism and mind games that go beyond normal cruelty. He becomes something of a Caligula or a Nero, a jaded yet almost childlike figure, gleefully watching The Teletubbies before ordering killings.
One of the questions about the possible return of The Master is whether he will be played with John Simm, with the same insanity, or whether he will be played by another actor, with another take on The Master's role as the devious tyrant.