Constraints are mathematical conditions that feasible solutions must satisfy. They represent: physical limitations (capacity, time), resource availability, logical requirements, quality standards, or policy rules. Types include: (1) Equality constraints: h(x) = 0; (2) Inequality constraints: g(x) ≤ 0 or g(x) ≥ 0; (3) Box constraints: lower ≤ x ≤ upper; (4) Integer/binary restrictions. Constraints define the feasible region. Active (binding) constraints at optimal solution have zero slack. Constraint formulation impacts solvability - tighter formulations with stronger linear programming relaxations improve performance. Techniques: constraint aggregation, valid inequalities, logical implications, and big-M formulations for conditional constraints.