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Numerous heating and cooling design methods, including energy storage, geothermal resources, heaters, solar collectors, underground water movement, lakes, and nuclear reactors, require the study of flow regimes in a cavity and their impact on thermal efficiency in heat transportation. Despite the existence of several review studies in the open literature, there is no specific review of heat transfer investigations that consider different cavity designs, such as spheres, squares, trapezoids, and triangles. Therefore, this work aims to conduct a comprehensive review of previous research published between 2016 and 2023 on heat transfer analysis in these cavity designs. The intention is to clarify how various cavity shapes perform in terms of flow and heat transfer, both with and without the addition of nano-enhanced phase change materials (NePCMs), which may include fins, obstacles, cylinders, and baffles. The study also explores the influence of factors like thermophoresis, buoyancy, magnetic forces, and others on heat transport in cavities. Additionally, it investigates the role of air, water, nanofluids, and hybrid nanofluids within cavities. According to the reviewed research, nanoparticles in the base fluid speed up the cooling process and reduce the required discharging time. Thermophoresis, where nanoparticles move from the heated wall to the cold nanofluid flow, becomes more pronounced with increasing Reynolds numbers. Increasing the heated area of the lower flat fin enhances the heat transfer rate, while increasing both the Rayleigh number and the solid volume percentage of nanoparticles reduces it. Radiation blockage alters the path of hot particles and affects the anticipated radiative amount. Optical thickness plays a role in rapidly cooling a medium, and partition thickness has the most significant effect on heat transport when the thermal conductivity ratio is low. Heat transmission is most improved when the Rayleigh number is high and the Richardson number is low.