Acceptability judgments are reports of a speaker’s or signer’s subjective sense of the well-formedness, nativeness, or naturalness of (novel) linguistic forms. Their value comes in providing data about the nature of the human capacity to generalize beyond linguistic forms previously encountered in language comprehension. For this reason, acceptability judgments are often also called grammaticality judgments (particularly in syntax), although unlike the theory-dependent notion of grammaticality, acceptability is accessible to consciousness. While acceptability judgments have been used to test grammatical claims since ancient times, they became particularly prominent with the birth of generative syntax. Today they are also widely used in other linguistic schools (e.g., cognitive linguistics) and other linguistic domains (pragmatics, semantics, morphology, and phonology), and have been applied in a typologically diverse range of languages. As psychological responses to linguistic stimuli, acceptability judgments are experimental data. Their value thus depends on the validity of the experimental procedures, which, in their traditional version (where theoreticians elicit judgments from themselves or a few colleagues), have been criticized as overly informal and biased. Traditional responses to such criticisms have been supplemented in recent years by laboratory experiments that use formal psycholinguistic methods to collect and quantify judgments from nonlinguists under controlled conditions. Such formal experiments have played an increasingly influential role in theoretical linguistics, being used to justify subtle judgment claims or new grammatical models that incorporate gradience or lexical influences. They have also been used to probe the cognitive processes giving rise to the sense of acceptability itself, the central finding being that acceptability reflects processing ease. Exploring what this finding means will require not only further empirical work on the acceptability judgment process, but also theoretical work on the nature of grammar.