Autophagosomes form in eukaryotic cells in response to starvation or to other stress conditions brought about by the unwanted presence in the cytosol of pathogens, damaged organelles or aggregated protein assemblies. The uniqueness of autophagosomes is that they form de novo and that they are the only double-membraned vesicles known in cells, having arisen from flat membrane sheets which have expanded and self-closed. The various steps describing their formation as well as most of the protein and lipid components involved have been identified. Furthermore, the hierarchical relationships among the components are well documented, and the mechanistic rationale for some of these hierarchies has been revealed. In the present review, we try to provide a current view of the process of autophagosome formation in mammalian cells, emphasizing along the way gaps in our knowledge that need additional work.