4. The Time War and the Daleks
The Time Lords' mortal enemy is a race of aliens called The Daleks. Driven by pure, unadulterated hatred and bent on the total annihilation of all life in the universe, the Daleks conquered much of space and finally surrounded the Time Lord homeworld of Gallifrey with their warships. Desperate not to let them win, The Doctor used an ancient weapon that destroyed his home planet, but took the entire Dalek fleet with it.
This war took place before the revival in 2005, serving as a delineation between new Who and classic Who. Since the series was started again, the Doctor has been haunted by survivor's guilt, knowing that he was responsible for the genocide of both his own race and the Daleks. (Even though the Daleks were evil, the Doctor had previously shied away from destroying them completely.) But as the show continued, it became clear that not all of the Daleks were destroyed... and even Gallifrey survived by being moved into a pocket universe and frozen in time. The Doctor doesn't know where Gallifrey is anymore, but he's looking.
Yes, the Daleks look like a giant pepper shaker with a toilet plunger and an egg beater stuck to them. (When they were introduced in 1963, the show was low budget. Really low budget.) And though they've kept the look, they come off as inhuman and thoroughly dangerous on the show -- so much so that they are considered the iconic villains of the series.
When a Time Lord dies, due to injury or old age, they return to life through a process called regeneration. They can do this 12 times for a total of 13 lives. Each time they regenerate, they appear with a different face and a somewhat altered personality, though they share the same memories. This, of course, made it easy for the BBC to replace the main actor and keep the franchise going -- a dilemma they were faced with when in 1966, first Doctor William Hartnell had to step down from the role due to deteriorating health.
The classic series ended with seven different actors having played the Doctor, an attempt to revive the series in 1996 with a TV movie gave us the Eighth Doctor, and the revived series has brought us Doctors Nine (Christopher Eccleston), Ten (David Tennant), Eleven (Matt Smith), and now Twelve (Peter Capaldi). And, yes, most fans refer to different incarnations of the Doctor by number.
The recent revelation that there was regeneration during the Time War -- between the Eighth and Ninth Doctors -- has thrown off the numbering, but most fans are keeping to the original system and simply referring to this in-between incarnation, played by John Hurt, as The War Doctor.
Because of the War Doctor regeneration, the so-called Eleventh Doctor had reached his final regeneration -- but at the last minute was granted another full regeneration cycle by the Time Lords.