Many practical, real-world applications have dynamic features. If the changes in the fitness function of an optimization problem are moderate, a complete restart of the optimization algorithm may not be warranted. In those cases, it is meaningful to apply optimization algorithms that can accommodate change. In the recent past, many researchers have contributed algorithms suited for dynamic problems. To facilitate the comparison between different approaches, the Moving Peaks (MP) function was devised. This chapter reviews all known optimization algorithms that have been tested on the dynamic MP problem. The majority of these approaches are nature-inspired. The results of the best-performing solutions based on the MP benchmark are directly compared and discussed. In the concluding remarks, the main characteristics of good approaches for dynamic optimization are summarised.