Macroautophagy (hereafter referred to as autophagy) degrades various intracellular constituents to regulate a wide range of cellular functions, and is also closely linked to several human diseases. In selective autophagy, receptor proteins recognize degradation targets and direct their sequestration by double-membrane vesicles called autophagosomes, which transport them into lysosomes or vacuoles. Although recent studies have shown that selective autophagy is involved in quality/quantity control of some organelles, including mitochondria and peroxisomes, it remains unclear how extensively it contributes to cellular organelle homeostasis. Here we describe selective autophagy of the endoplasmic reticulum (ER) and nucleus in the yeast Saccharomyces cerevisiae. We identify two novel proteins, Atg39 and Atg40, as receptors specific to these pathways. Atg39 localizes to the perinuclear ER (or the nuclear envelope) and induces autophagic sequestration of part of the nucleus. Atg40 is enriched in the cortical and cytoplasmic ER, and loads these ER subdomains into autophagosomes. Atg39-dependent autophagy of the perinuclear ER/nucleus is required for cell survival under nitrogen-deprivation conditions. Atg40 is probably the functional counterpart of FAM134B, an autophagy receptor for the ER in mammals that has been implicated in sensory neuropathy. Our results provide fundamental insight into the pathophysiological roles and mechanisms of 'ER-phagy' and 'nucleophagy' in other organisms.