Several independent groups have published that autophagy is required for optimal RNA replication of dengue virus (DENV). Initially, it was postulated that autophagosomes might play a structural role in replication complex formation. However, cryo-EM tomography of DENV replication complexes showed that DENV replicates on endoplasmic reticulum (ER) cisternae invaginations and not on classical autophagosomes. Recently, it was reported that autophagy plays an indirect role in DENV replication by modulating cellular lipid metabolism. DENV-induced autophagosomes deplete cellular triglycerides that are stored in lipid droplets, leading to increased β-oxidation and energy production. This is the first example of a virus triggering autophagy to modulate cellular physiology. In this review, we summarize these data and discuss new questions and implications for autophagy during DENV replication.