Abstract: Natural convection in an enclosure (internal convection) is an important problem due to its significant practical applications. In energy related applications, natural convection plays a dominant role in transport of energy for the proper design of enclosures in order to achieve higher heat transfer rates. This review summarizes the studies on natural convection heat transfer in triangular, trapezoidal, parallelogrammic enclosures and enclosures with curved and wavy walls filled with fluid or porous media. In addition, this review also summarizes the natural convection studies in the nanofluid filled enclosures. Studies have been performed for the enclosures subjected to different thermal boundary conditions. A number of the studies demonstrated that the variation of the aspect ratio and base angle of the triangular and rhombic/parallelogrammic enclosures had a wide influence on the flow distribution pattern. In the trapezoidal enclosure, the aspect ratio of the cavity as well as the presence of the baffles along the walls played a significant role in the temperature and flow distribution. The flow patterns within the complex enclosures were found to be largely dependent on the amplitude-wavelength ratio and number of undulations of the wavy walls. In addition, the researchers have also studied the effect of the various parameters such as the Rayleigh numbers, Prandtl numbers, Darcy numbers, Darcy–Rayleigh number, irreversibility distribution ratios, volume fraction of the nanoparticles, etc. Overall, the current review paper presents an useful insight into the potential strategies for enhancing the convection heat transfer performance.