A state-of-the-art review is provided for analyses on sidewall-heated natural convection flows in an enclosure. Particular emphasis is given to those subjected to nonideal physical conditions. Delineation is made of the effects of thermal boundary conditions with substantial spatial and temporal variations. Specifically, four topical issues are considered: the finiteness of thermal conductance of the solid walls, the variable physical properties of the fluid, time-dependent thermal loading on the surface walls, and finally, the three-dimensionalities. In the present article, the main focus is placed on laminar flows in a rectangular cavity. This reveals salient flow features while disallowing distractions due to other complexities. Discrepancies between the preceding conventional two-dimensional numerical predictions with idealized boundary conditions and the available experimental measurements are highlighted. These may be attributable to the unexplored aspects of realistic flows, and parts of these are explicitly discussed here.