Doctor Who/Recap/S9/E01 Day of the Daleks

You don't understand. No-one who didn't live through those terrible years can understand. Towards the end of the 20th Century, a series of wars broke out. There were hundreds of years of nothing but destruction and killing. Nearly seven eighths of the world's population wiped out. The rest living in holes in the ground, starving, almost reduced to the level of animals...

—The Controller tries to justify collaborating with the Daleks.

Before The Terminator, there was Day of the Daleks.

A peace conference is being held in Britain under the auspices of Sir Reginald Styles - it's a reconvening of the one from "The Mind of Evil", and UNIT are once again providing security. Because they did such a bang-up job previously.

Anyhow, Styles is attacked and nearly killed by a guerrilla fighter in futuristic dress, but is saved by the intervention of a big - well - gorilla fighter, who knocks the assassin out and disappears. The Doctor deduces that the unconscious man is from the future, and that a device found with him is a time-travel gadget.

The Doctor poses as Styles in order to catch the assailants. They try again, but the Doctor convinces them he's not Styles. Jo accidentally activates one of the time-travel gadgets and zaps herself into the 22nd century, and the Doctor and the guerrillas follow her. One of the guerrillas, Shura, is injured and is left behind for treatment.

We discover that in this future, the Earth is ruled by the Daleks, using their ape-like Ogron subjects as heavies. There are also human collaborators, led by "the Controller". Jo and the Doctor are taken prisoner at the Dalek base, but rescued by the guerrillas - who finally get round to explaining that they're trying to kill Styles because they believe he blew up the peace conference, which started a series of wars leaving Earth shattered and ripe for Dalek conquest. They mean to kill Styles first and change "history".

The Doctor realises that this is a Stable Time Loop - that the explosion was actually caused by the guerrillas: specifically by Shura, the injured man left behind in the 20th century, trying to fulfill his mission. He gets back to the 20th century in time to have Styles' house evacuated and the pursuing Daleks and Ogrons are destroyed when Shura detonates his bomb.

Tropes

An Astral Projection, Not a Ghost: The ghosts the Doctor is asked to investigate turn out to be projections of time travellers from the future.
Bound and Gagged: This is the ONLY serial in the entire run of Doctor Who where both the Doctor and his companion (Jo Grant) are bound and gagged.
Crapsack World: Future version of Earth, ruled by Daleks
Hollywood Darkness: "We'll wait 'til it's light", says the time traveller who's just materialised in broad daylight. No attempt is made to match the lighting to the dialogue in this scene.
Killer Space Monkey: The Ogrons, dim-witted mooks of the Daleks, put on their first appearance.
La Résistance
Oh Crap: The Daleks get one when they discover that Jo isn't on her own.

Controller: The girl referred to a companion in her own time zone. She called him... "the Doctor".
Dalek: Doc-tor? Did you say "Doc-tor"?!

Panty Shot: Well what do you think happens when Jo climbs down a long ladder whilst wearing a miniskirt?
Pillar of Light: In the DVD special edition, the Daleks' Time Vortex Magnetron creates one.
The Quisling: The Controller, though he also fulfils the Redemption Equals Death trope.

Daleks: "YOU HAVE BETRAYED THE DALEKS! EXTERMINATE! EXTERMINATE!"
Controller: "Who knows, I might have helped to exterminate you!"