Macroautophagy/autophagy is a key catabolic process, essential for maintaining cellular homeostasis and survival through the removal and recycling of unwanted cellular material. Emerging evidence has revealed intricate connections between the RNA and autophagy research fields. While a majority of studies have focused on protein, lipid and carbohydrate catabolism via autophagy, accumulating data supports the view that several types of RNA and associated ribonucleoprotein complexes are specifically recruited to phagophores (precursors to autophagosomes) and subsequently degraded in the lysosome/vacuole. Moreover, recent studies have revealed a substantial number of novel autophagy regulators with RNA-related functions, indicating roles for RNA and associated proteins not only as cargo, but also as regulators of this process. In this review, we discuss widespread evidence of RNA catabolism via autophagy in yeast, plants and animals, reviewing the molecular mechanisms and biological importance in normal physiology, stress and disease. In addition, we explore emerging evidence of core autophagy regulation mediated by RNA-binding proteins and noncoding RNAs, and point to gaps in our current knowledge of the connection between RNA and autophagy. Finally, we discuss the pathological implications of RNA-protein aggregation, primarily in the context of neurodegenerative disease.