Social contract theory grounds the legitimacy of government in an agreement, usually hypothetical, among free individuals about the terms of their common life. Its power is that it makes political authority answerable to those subject to it without requiring that they actually consented to anything. The test is what they could not reasonably reject.
Hobbes invented the framework in Leviathan (1651) and used it to defend nearly absolute sovereignty. Rational individuals in a state of mutual fear would trade almost all liberty for security, and having done so could not complain of the bargain. Locke turned the same device against absolutism in 1689, arguing that people carry natural rights into political society and keep a right of resistance when government violates the trust. Rousseau radicalized it into popular sovereignty: legitimate law is what a people gives itself, and sovereignty cannot be represented. Kant then recast the contract as a standard of public reason instead of an event.
Rawls revived the tradition decisively in 1971 with the original position, asking what principles of justice people would choose behind a veil of ignorance about their own place in society. The device made distributive justice a contractarian question for the first time, and most subsequent work is a response to it: Nozick objecting that the argument licenses continuous interference with holdings, Gauthier attempting to derive morality from bargaining alone, Scanlon reformulating it around reasonable rejection.
Hume made the standing objection before the tradition had finished forming. No such contract ever occurred; tacit consent inferred from residence is not consent; and the obligations the contract is meant to explain are ones we already recognize on other grounds. Later critics argued that the abstraction hides who was actually party to the bargain. Pateman on the sexual contract and Mills on the racial one both point out that the contracts really made were between some men about the standing of everyone else.