This paper considers the role of school closures in the spread of the SARS-CoV-2 virus. To isolate the impact of the closures from other containment measures and identify a causal effect, we exploit variation in the start and end dates of the summer and fall school holidays across the 16 federal states in Germany using a difference-in-differences design with staggered adoption. We show that neither the summer closures nor the closures in the fall had a significant containing effect on the spread of SARS-CoV-2 among children or a spill-over effect on older generations. There is also no evidence that the return to school at full capacity after the summer holidays increased infections among children or adults. Instead, we find that the number of children infected increased during the last weeks of the summer holiday and decreased in the first weeks after schools reopened, a pattern we attribute to travel returnees.