The selective clearance of organelles by autophagy is critical for the regulation of cellular homeostasis in organisms from yeast to humans. Removal of damaged organelles clears the cell of potentially toxic byproducts and enables reuse of organelle components for bioenergetics. Thus, defects in organelle clearance may be detrimental to the health of the cells, contributing to cancer, neurodegeneration, and inflammatory diseases. Organelle-specific autophagy can clear mitochondria, peroxisomes, lysosomes, ER, chloroplasts, and the nucleus. Here, we review our understanding of the mechanisms that regulate the clearance of organelles by autophagy and highlight gaps in our knowledge of these processes.