For example, if the government of the United States was overthrown tomorrow, and replaced by a newly formed Kingdom of Ongo Bongo, all of the previously controlled territory, weapons, and wealth of the former U.S. government would fall under the control of the government of the new Kingdom. In other words, the new state of Ongo Bongo would (at least initially) assume all the powers of the state it just demolished.
The theory has its root in 19th century diplomacy. Some critics argue the succession theory is weak for it allows few boundaries between eras allowing archaic claims to subvert popular will.
In general the theory is followed in the world community: a new government might be distasteful to others but pragmatically it must be recognized if it de facto controls the territory. There are several fairly recent examples where succession has not been smoothly adhered to: