Autophagy is a catabolic process that has been implicated both as a tumor suppressor and in tumor progression. Here, we investigate this dichotomy in cancer biology by studying the influence of altered autophagy in Drosophila models of tissue overgrowth. We find that the impact of altered autophagy depends on both genotype and cell type. As previously observed in mammals, decreased autophagy suppresses Ras-induced eye epithelial overgrowth. In contrast, autophagy restricts epithelial overgrowth in a Notch-dependent eye model. Even though decreased autophagy did not influence Hippo pathway-triggered overgrowth, activation of autophagy strongly suppresses this eye epithelial overgrowth. Surprisingly, activation of autophagy enhanced Hippo pathway-driven overgrowth in glia cells. These results indicate that autophagy has different influences on tissue growth in distinct contexts, and highlight the importance of understanding the influence of autophagy on growth to augment a rationale therapeutic strategy.