Multi-start procedures were originally conceived as a way to exploit a local or neighborhood search procedure, by simply applying it from multiple random initial solutions. Modern multi-start methods usually incorporate a powerful form of diversification in the generation of solutions to help overcome local optimality. Different metaheuristics, such as GRASP or tabu search, have been applied to this end. This survey briefly sketches historical developments that have motivated the field and then focuses on modern contributions that define the current state of the art. Two classical categories of multi-start methods are considered according to their domain of application: global optimization and combinatorial optimization. Additionally, several methods are reviewed to estimate the number of local optima in combinatorial problems. The estimation of this number can help to establish the complexity of a given instance, and also to choose the most convenient neighborhood, which is especially interesting in the context of multi-start methods. Experiments on three well-known combinatorial optimization problems are included to illustrate the local optima estimation techniques.