David Tennant, the Tenth Doctor, had several predictions that "His song was ending," but no one guessed how. It wasn't The Master or The Gallifreyans killing him, it was rescuing Wilfred Mott from a huge dose of radiation by absorbing it himself. Still, he had some time left and used it to take a farewell tour of his past companions. He saved Martha and her husband Mickey (They decided to hyphenate so it was Martha Smith-Jones.) from being killed by Sontarons, saved Sarah Jane's son Luke from being run over by a car, found Captain Jack a good companion, and got Donna what she thought was a really punk wedding present, a lottery ticket!
Several times during these farewell scenes the Doctor says something about, "Getting his reward," but what is the reward? It's never overtly explained, but it's probably permission to violate the Laws of Time to help his past companions. But if so, who's high enough on the universal totem pole to give the Doctor permission to violate the Time Laws? Or did he just decide to do these things on his Own? Probably not, since he didn't say "Taking his reward," he said "Getting it."These little mysteries are one of the most charming aspects of Dr Who. Us Who-Nerds are always hoping these things will be resolved in future stories but they often aren't.
There are some loose ends concerning the Mott family and the Nobel family. The Doctor mentions borrowing a quid in the past from a Jeffrey Nobel who appears to be Donna's father. The mystery woman who communicates with Wilfred seems to be a Time Lord, maybe the Doctor's mother, maybe even a far future version of River-Song, but why Wilfred Mott? The families seem to be connected to the Doctor in ways that neither understand. If that connection extends to the Eleventh Doctor, maybe we'll find out.
The Tenth Doctor finally ended up in the TARDIS and after the usual light show, and explosions, and fade out and fade in, became...
The Eleventh Doctor, Matt Smith. Matt got off to a good start by doing a self-examination to see if he had all the correct body parts (lots of fingers). When he got to his hair he said, "I'm a girl!" Nope, better luck next time. Matt was very upbeat in contrast to the Tenth Doctor who was morose at having to cash in his chips at the tender young age of only 906. Well, who could blame him? Anyway the Eleventh Doctor is off and running.