Recent advances in deep learning promote the innovation of many intelligent systems and applications such as autonomous driving and image recognition. Despite enormous efforts and investments in this field, a fundamental question remains under-investigated - what challenges do developers commonly face when building deep learning applications? To seek an answer, this paper presents a large-scale empirical study of deep learning questions in a popular Q&A website, Stack Overflow. We manually inspect a sample of 715 questions and identify seven kinds of frequently asked questions. We further build a classification model to quantify the distribution of different kinds of deep learning questions in the entire set of 39,628 deep learning questions. We find that program crashes, model migration, and implementation questions are the top three most frequently asked questions. After carefully examining accepted answers of these questions, we summarize five main root causes that may deserve attention from the research community, including API misuse, incorrect hyperparameter selection, GPU computation, static graph computation, and limited debugging and profiling support. Our results highlight the need for new techniques such as cross-framework differential testing to improve software development productivity and software reliability in deep learning.