Metal-organic framework (MOF)-based composites have the inherent morphological features of MOF, including controllable, uniform pores, a large surface area, a clearly defined crystal structure, and so on. Depending on the metals and ligands used in MOF and the kinds of functional groups added to MOF-based compounds, these composites can be used for a wide range of reactions, such as hydroxylation, CO reduction, CO2 conversion, CO2 adsorption, separation, cycloaddition, etc. In that scenario, several properties like weak catalytic activities, lower cyclic stability, and poor electrochemical performances limit the industrial-scale uses of those compounds. This leads to more attention among industrial and academic researchers to explore more ways to overcome the drawbacks of MOF-based materials. Considering their morphological and structural characteristics, these composites are mostly used for heterogeneous catalytic reactions. The aim of this review is to highlight the fundamental concepts of MOFs, encompassing their structural and morphological characteristics, alongside approaches for their conversion into composites. Additionally, this study emphasizes the recent advancements in heterogeneous catalytic performance and the use of MOF-based composites in catalytic, electrical, and optical applications. The subsequent section delves into an examination of the future problems and prospects associated with MOF-based composites. This review would help new readers grasp MOFs so they can enjoy their catalytic performances.