The family of arguments that grounds political authority in some form of agreement — real, hypothetical, or rational — among those who are to be governed by it. Its question is the most basic in political philosophy: why should I obey? The contractarian answer is that legitimate authority rests, in the end, on something the governed could consent to.
The modern tradition has three canonical voices, and each gives the idea a different shape. Thomas Hobbes used the contract to justify near-absolute sovereignty — we contract out of the state of nature because any stable authority is better than none. John Locke used it to justify limited government bound by natural rights, with a reserved right of resistance when those rights are violated. Jean-Jacques Rousseau radicalized it into a theory of popular sovereignty: citizens obey only the laws they give themselves through the general will.
The idea went into eclipse in the 19th century under utilitarian and historicist attack — Jeremy Bentham thought it a fiction, Hegel and the historicists thought it naive — and roared back in the 20th through John Rawls's A Theory of Justice (1971), which reimagined the contract as a device of representation: principles of justice are those we would choose behind a "veil of ignorance" about our own position in society.
Its persistent critics point out that no actual contract was ever signed and that real consent is hard to locate. Contractarians reply that the point is not historical but normative — a test of what political arrangements can be justified to those they bind.