Autophagy is directed by numerous distinct autophagy-related (Atg) proteins. These transmit starvation-induced signals to lipids and regulatory proteins and assemble a double-membrane autophagosome sequestering bulk cytoplasm and/or selected cargos destined for degradation upon autophagosome fusion with a vacuole or lysosome. This Review discusses the structural mechanisms by which Atg proteins sense membrane curvature, mediate a PI(3)P-signaling cascade, and utilize autophagy-specific ubiquitin-like protein cascades to tether proteins to autophagosomal membranes. Recent elucidation of molecular interactions enabling vesicle nucleation, elongation, and cargo recruitment provides insights into how dynamic protein-protein and protein-membrane interactions may dictate size, shape, and contents of autophagosomes.