Constraint satisfaction problems (CSPs) define states as assignments of variables to values from their domains, with constraints specifying allowable combinations. Backtracking search assigns one variable at a time using depth-first search. Improved heuristics like most-constrained variable selection and least-constraining value choice help. Forward checking and constraint propagation techniques like arc consistency detect inconsistencies earlier than backtracking alone. Local search methods like min-conflicts hill-climbing can also solve CSPs by allowing constraint violations and minimizing them.