Narrowly speaking, the correspondence theory of truth is the view that truth is correspondence to, or with, a fact—a view that was advocated by Russell and Moore early in the 20th century. But the label is usually applied much more broadly to any view explicitly embracing the idea that truth consists in a relation to reality, i.e., that truth is a relational property involving a characteristic relation (to be specified) to some portion of reality (to be specified). This basic idea has been expressed in many ways, giving rise to an extended family of theories and, more often, theory sketches. Members of the family employ various concepts for the relevant relation (correspondence, conformity, congruence, agreement, accordance, copying, picturing, signification, representation, reference, satisfaction) and/or various concepts for the relevant portion of reality (facts, states of affairs, conditions, situations, events, objects, sequences of objects, sets, properties, tropes). The resulting multiplicity of versions and reformulations of the theory is due to a blend of substantive and terminological differences.
The correspondence theory of truth is often associated with metaphysical realism. Its traditional competitors, pragmatist, as well as coherentist, verificationist, and other epistemic theories of truth, are often associated with idealism, anti-realism, or relativism. In recent years, these traditional competitors have been virtually replaced (at least from publication-space) by deflationary theories of truth and, to a lesser extent, by the identity theory (note that these new competitors are typically not associated with anti-realism). Still more recently, two further approaches have received considerable attention. One is truthmaker theory: it is sometimes viewed as a competitor to, sometimes as a more liberal version of, the correspondence theory. The other is pluralism: it incorporates a correspondence account as one, but only one, ingredient of its overall account of truth.
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