There exists a great diversity of buoyancy flows in enclosures that are of interest in science and technology. These buoyancy flows pose new and challenging physical and mathematical problems. Emphasis is given to the complexities of the phenomena, viz., the coupling of the flow and transport and of the boundary-layer and core flows, the interaction between the flow and the driving force, which alters the regions in which the buoyancy acts, and the occurrence of flow sub-regions (cells and layers). The importance of scaling analysis and experiments to determine flow details are discussed and the essentials of scaling techniques are outlined. The implications of these for numerical methods are presented, and the inadequacies of purely numerical solutions are pointed out. Representative works covering a broad range of problems are discussed.