Deep learning has recently become very popular on account of its incredible success in many complex data-driven applications, such as image classification and speech recognition. The database community has worked on data-driven applications for many years, and therefore should be playing a lead role in supporting this new wave. However, databases and deep learning are different in terms of both techniques and applications. In this paper, we discuss research problems at the intersection of the two fields. In particular, we discuss possible improvements for deep learning systems from a database perspective, and analyze database applications that may benefit from deep learning techniques. Database Meets Deep Learning: Challenges and Opportunities