Centronuclear myopathies (CNMs) are genetic diseases whose symptoms are muscle weakness and atrophy (wasting) and centralised nuclei. Recent human genetic studies have isolated several groups of mutations. Among them, many are found in two interacting proteins essential to clathrin-mediated endocytosis, dynamin and the BIN-Amphiphysin-Rvs (BAR) protein BIN1/amphiphysin 2. In this review, by using structural and functional data from the study of endocytosis mainly, we discuss how the CNM mutations could affect the structure and the function of these ubiquitous proteins and cause the muscle-specific phenotype. The literature shows that both proteins are involved in the plasma membrane tubulation required for T-tubule biogenesis. However, this system also requires the regulation of the dynamin-mediated membrane fission, and the formation of a stable protein-scaffold to maintain the T-tubule structure. We discuss how the specific functions, isoforms and partners (myotubularin in particular) of these two proteins can lead to the establishment of muscle-specific features.