The challenge of maximizing the diversity of a collection of points arises in a variety of social studies, which translates into the growing interest in the treatment of diversity in mathematical models. Although the terms diversity and dispersion can be found in many optimization problems to be indistinguishable, we undertake to explore the different models behind them. This chapter describes the mathematical models for two diversity problems and three equity problems. In addition, it also includes two related models that have recently received special attention. This chapter also reviews heuristics and metaheuristics for finding near-optimal solutions for these problems, such as GRASP, Tabu Search, Genetic algorithms, Particle Swarm, and Ant Colony Optimization. We include pseudocodes of some of these methods.