The study of fluid flows in a cavity and their effect on thermal performance in heat transporting and entropy generation are found in many heating and cooling engineering applications such as energy storage geothermal reservoirs, boilers, solar collectors, underground water flow, lakes, nuclear reactors. This paper presents a comprehensive review of the recent numerical and experimental studies on both heat transfer and entropy generation and their applications in cavities. The effect of the fluid thermal properties, the cavity configuration, the boundary, and initial conditions, the magnetic field, the thermal source discretion, and other geometrical and physical parameters on heat transfer and entropy generation are discussed. This study also presents the effect of several important dimensionless parameters such as the Reynolds, Richardson, Grashof, Rayleigh, Darcy, Hartmann, and Prandtl numbers on both natural and combined convection heat transfer mechanisms in cavities. © 2021, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.