Constraint programming is a programming paradigm where relations between variables can be stated in the form of constraints. Constraints differ from the common primitives of other programming languages in that they do not specify a step or sequence of steps to execute but rather the properties of a solution to be found. The constraints used in constraint programming are of various kinds: those used in constraint satisfaction problems, those solved by the simplex algorithm, and others.

Constraints are usually embedded within a programming language or provided via separate software libraries. Constraint satisfaction problems or CSPs are mathematical problems where one must find states or objects that satisfy a number of constraints or criteria. CSPs are the subject of intense research in both artificial intelligence and operations research. Many CSPs require a combination of heuristics and combinatorial search methods to be solved in a reasonable time.

Most classes of CSPs that are known to be tractable are those where the hypergraph of constraints has bounded treewidth (and there are no restrictions on the set of constraint relations), or where the constraints have arbitrary form but there exist essentially non-unary polymorphisms of the set of constraint relations.