Autophagy delivers cytoplasmic components and organelles to lysosomes for degradation. This pathway serves to degrade nonfunctional or unnecessary organelles and aggregate-prone and oxidized proteins to produce substrates for energy production and biosynthesis. Macroautophagy delivers large aggregates and whole organelles to lysosomes by first enveloping them into autophagosomes that then fuse with lysosomes. Chaperone-mediated autophagy (CMA) degrades proteins containing the KFERQ-like motif in their amino acid sequence, by transporting them from the cytosol across the lysosomal membrane into the lysosomal lumen. Autophagy is especially important for the survival and homeostasis of postmitotic cells like neurons, because these cells are not able to dilute accumulating detrimental substances and damaged organelles by cell division. Our current knowledge on the autophagic pathways and molecular mechanisms and regulation of autophagy will be summarized in this review. We will describe the physiological functions of macroautophagy and CMA in neuronal cells. Finally, we will summarize the current evidence showing that dysfunction of macroautophagy and/or CMA contributes to neuronal diseases. We will give an overview of our current knowledge on the role of autophagy in aging neurons, and focus on the role of autophagy in four types of neurodegenerative diseases, i.e., amyotrophic lateral sclerosis and frontotemporal dementia, prion diseases, lysosomal storage diseases, and Parkinson's disease.