Two-dimensional (2D)/quasi-2D organic-inorganic halide perovskites are regarded as naturally formed multiple quantum wells with inorganic layers isolated by long organic chains, which exhibit layered structure, large exciton binding energy, strong nonlinear optical effect, tunable bandgap via changing the layer number or chemical composition, improved environmental stability, and excellent optoelectronic properties. The extensive choice of long organic chains endows 2D/quasi-2D perovskites with tunable electron-phonon coupling strength, chirality, or ferroelectricity properties. In particular, the layered nature of 2D/quasi-2D perovskites allows us to exfoliate them to thin plates to integrate with other materials to form heterostructures, the fundamental structural units for optoelectronic devices, which would greatly extend the functionalities in view of the diversity of 2D/quasi-2D perovskites. In this paper, the recent achievements of 2D/quasi-2D perovskite-based heterostructures are reviewed. First, the structure and physical properties of 2D/quasi-2D perovskites are introduced. We then discuss the construction and characterizations of 2D/quasi-2D perovskite-based heterostructures and highlight the prominent optical properties of the constructed heterostructures. Further, the potential applications of 2D/quasi-2D perovskite-based heterostructures in photovoltaic devices, light emitting devices, photodetectors/phototransistors, and valleytronic devices are demonstrated. Finally, we summarize the current challenges and propose further research directions in the field of 2D/quasi-2D perovskite-based heterostructures.