Three-dimensional images of mitochondria provided by electron tomography reveal that the micro-compartments (cristae) defined by the inner membrane are connected to the periphery of this membrane by narrow tubular junctions, which likely restrict diffusion. The tomograms also strongly suggest that inner membrane topology represents a balance between membrane fusion and fission processes. The hypothesis being developed is that inner membrane topology is a regulated property of mitochondria. This review summarizes the evidence about how inner membrane shape influences mitochondrial function and, conversely, what is known about the factors that determine this membrane's topology.