We propose a new conflict-driven program synthesis technique that is capable of learning from past mistakes. Given a spurious program that violates the desired specification, our synthesis algorithm identifies the root cause of the conflict and learns new lemmas that can prevent similar mistakes in the future. Specifically, we introduce the notion of equivalence modulo conflict and show how this idea can be used to learn useful lemmas that allow the synthesizer to prune large parts of the search space. We have implemented a general-purpose CDCL-style program synthesizer called Neo and evaluate it in two different application domains, namely data wrangling in R and functional programming over lists. Our experiments demonstrate the substantial benefits of conflict-driven learning and show that Neo outperforms two state-of-the-art synthesis tools, Morpheus and Deepcoder, that target these respective domains.