Autophagy is a major catabolic pathway in eukaryotes, which is required for the lysosomal/vacuolar degradation of cytoplasmic proteins and organelles. Interest in the autophagy pathway has recently gained momentum largely owing to identification of multiple autophagy-related genes and recognition of its involvement in various physiological conditions. Here we review current knowledge of the molecular mechanisms regulating autophagy in mammals and yeast, specifically the biogenesis of autophagosomes and the selectivity of their cargo recruitment. We discuss the different steps of autophagy, from the signal transduction events that regulate it to the completion of this pathway by fusion with the lysosome/vacuole. We also review research on the origin of the autophagic membrane, the molecular mechanism of autophagosome formation, and the roles of two ubiquitin-like protein families and other structural elements that are essential for this process. Finally, we discuss the various modes of autophagy and highlight their functional relevance for selective degradation of specific cargos.