As an alternative to analytical methods, which could be difficult to apply, evolutionary methods give good success opportunities for many types of optimization scenarios. Evolutionary methods can escape from local traps, which is an important feature. Being so many the algorithms that had been proposed, we devoted three chapters to evolutionary methods. To begin with, the simulated annealing method has been chose, being an algorithm inspired in physics and not in biology. Tabu search is introduced next, trying not to explore several times the same place. As an application example, we used simulated annealing for a travelling salesman problem. In the next section, an archetype of bio-inspired methods is chosen: the genetic algorithms. Continuing with related ideas, the next section introduces genetic programming (programs are built by joining pieces), evolution strategies, and differential evolution. Another section introduces now the particle swarm optimization (PSO), inspired in bird flocks and other collective behaviors in Nature. Finally, the chapter introduces the ant colonies algorithm, in which we have some experience. Ants constitute a metaphor that highlights the importance of balancing exploration and exploitation. As usual in this book, the chapter includes several programs in MATLAB.