Microplastics (MPs) are currently a serious environmental problem, primarily due to their persistence in the environment, low concentration, and difficulty in detection and disposal. MPs have also been detected in humans and have been shown to be harmful. Although there are methodologies for their recovery or elimination in most water treatment plants, a significant portion still bypasses these elimination systems. It is this percentage that we must try to eliminate. In addition to finding new methodologies for the treatment of MPs, it is important to find new materials adapted to this process. In this context, metal–organic frameworks (MOFs) are high-versatility compounds that can be synthesized using different techniques to obtain materials with different properties, such as porosity, morphology, conductivity, etc. These materials can adsorb MPs in different ways, such as electrostatic interaction, bond formation, etc., or they can be obtained by containing metals that catalyze reactions for the formation of highly reactive species that can oxidize the MPs. This review examines how MOF materials have gained attention for the adsorption-based recovery and removal of MPs and discusses the problems associated with these materials and possible solutions.