SUMMARYThis article reviews a recent body of work that documents the heat #ow through walls with relatively complicated internal structure. The "rst part presents the fundamentals of natural convection heat transfer in two-dimensional enclosures "lled with air. Numerical simulations for Rayleigh numbers in the range 6000}30000 and aspect ratio A"40 show that the air circulation is periodic (pulsating) and the core space is dominated by almost equidistant rolls. The heat transfer e!ected by such #ows is documented, and the application to walls with tall cavities (hollow bricks) is discussed. The paper continues with a study of heat transfer through a ventilated wall heated by solar radiation from the side. The heated side is ventilated by an air channel opened at both ends. It is shown that the design of the air channel has a signi"cant e!ect on the share of the radiative heat input intercepted by the air #ow. The concluding part of the paper is a "rst-time review of new work on natural convection heat transfer across elongated vertical cavities with deformed side walls (e.g. air gaps in double-pane windows). It is shown that when the side walls are bent inward so that the cavity is narrower at mid-height than at its top and bottom ends, the total heat transfer rate through the system is increased signi"cantly. The deformation of the walls also a!ects the intensity and structure of the buoyancy-driven #ow in the air space. Overall, this article reviews some of the newest work on heat losses through complicated wall structures and projects it on the background provided by the existing literature. The global interest in energy conservation has stimulated a steady stream of fundamental and applied studies on how energy is lost*how heat &leaks'*from the systems in which energy currents are essential. Key advances are cited in the next section. This activity has placed the focus on the interaction between energy systems and their immediate #uid environments. The #ow of energy (heating) drives the #ow of #uids, and, in turn, #owing #uids convect energy. To predict the rate of heat loss e!ected by #uid #ow is one goal. Another is to interpret this result for the purpose of design: the development of structural changes in the wall of the system so that in future designs the loss of heat is minimized. The work reviewed in this article covers both aspects with application to the loss of heat through walls of buildings. The same mechanism, or the same &coupling' between #owing energy currents and #owing #uids stands behind the large-scale environmental #ows reviewed in other articles in this issue.