As the requirements in our daily lives and industrial production become diverse, a single solution cannot meet their demands anymore. Multimodal optimization can provide multiple feasible solutions. However, most of the previous researches on multimodal optimization focus on single-objective optimization. In fact, there are multimodal problems in multiobjective optimization, which, have multiple local or global Pareto sets and it is of great theoretical and practical significance to find these Pareto sets. Therefore, first, this paper introduces the features and challenges of multimodal multiobjective problems. Second, a survey on existing multimodal multiobjective optimization algorithms is given. Third, multimodal multiobjective benchmark problems and performance indicators are introduced. Finally, the applications and future research works are given.