Greedy randomized adaptive search procedure (GRASP) is a metaheuristic framework which has been extensively used for solving a wide variety of hard combinatorial optimization problems. Several diversity maximization problems have considered GRASP either as the main metaheuristic or even as a part of a hybrid algorithm, mainly due to its versatility to be adapted to any optimization problem. This chapter is focused on reviewing the most recent works considering GRASP for maximizing diversity and proposing a basic design and implementation of GRASP in the context of diversity problems. The resulting design is evaluated over the MDPLIB 2.0, which has become a de facto standard test bed for this family of problems.