One of the most peculiar membrane shapes is observed in mitochondria. These organelles are surrounded by two membranes and especially the convoluted inner membrane displays a complex ultra-structure. A molecular understanding of how this membrane is shaped is missing to a large extent. Unlike membrane remodeling in classical curvature-dependent processes like clathrin-mediated endocytosis, mitochondria are most likely shaped by integral membrane proteins. Following, we will review the current knowledge of inner mitochondrial membrane architecture and discuss recent findings and advances in understanding the factors that shape this membrane. We will address pending questions especially with regard to the experimentally challenging nature of investigating membrane bending by hydrophobic integral membrane proteins.