The design of exact algorithms running in polynomial time for problems belonging to the class NP-hard has been one of the main open problems in the area of theoretical computer science. For this reason, when one needs to solve instances of these problems that are sufficiently large, it is necessary to employ methods that may result only in an approximate solution. This chapter discusses metaheuristic strategies that are commonly used in the solution of hard combinatorial optimization problems. Approximation algorithms with performance guarantees offer a powerful approach to tackling NP-hard problems, providing solutions that are provably close to optimal. However, the design of such algorithms relies heavily on the specific properties of the problem and may not be generalizable across different problem domains. For problems where no approximation guarantee is feasible, heuristic methods remain an essential tool in the practitioner’s arsenal.