The Four Horsemen of the Apocalypse (The Book of Revelation) are Conquering, Disease, Famine and Death.
To conquer a power, one must occupy all cities of that power.
The conquered player is eliminated, and all the provinces of that power become the conqueror's. All income from the provinces and cities revert to the conqueror.
They may strategically move to and within, and build military units in those provinces.
To be conquered, you must lose their original provinces and any acquired through conquest.