We survey neurosymbolic program synthesis, an emerging research area at the interface of deep learning and symbolic artificial intelligence. As in classical machine learning, the goal in neurosymbolic program synthesis is to learn functions from data. However, these functions are represented as programs that use symbolic primitives, often in conjunction with neural network components, and must, in some cases, satisfy certain additional behavioral constraints. The programs are induced using a combination of symbolic search and gradient-based optimization. In this survey, we categorize the main ways in which symbolic and neural learning techniques come together in this area. We also showcase the key advantages of the approach — specifically, greater reliability, interpretability, verifiability, and compositionality — over end-to-end deep learning.