Synthetic biology has a natural synergy with deep learning. It can be used to generate large data sets to train models, for example by using DNA synthesis, and deep learning models can be used to inform design, such as by generating novel parts or suggesting optimal experiments to conduct. Recently, research at the interface of engineering biology and deep learning has highlighted this potential through successes including the design of novel biological parts, protein structure prediction, automated analysis of microscopy data, optimal experimental design, and biomolecular implementations of artificial neural networks. In this review, we present an overview of synthetic biology-relevant classes of data and deep learning architectures. We also highlight emerging studies in synthetic biology that capitalize on deep learning to enable novel understanding and design, and discuss challenges and future opportunities in this space.