Reaction and retrosynthesis prediction are two fundamental tasks in computational chemistry. In recent years, these two tasks have attracted great attentions from both machine learning and drug discovery communities. Various deep learning approaches have been proposed to tackle these two problems and achieved initial success. In this survey, we conduct a comprehensive investigation on advanced deep learning-based reaction and retrosynthesis prediction models. We first summarize the design mechanism, strengths and weaknesses of the state-of-the-art approaches. Then we further discuss limitations of current solutions and open challenges in the problem itself. Last but not the least, we present some promising directions to facilitate future research. To our best knowledge, this paper is the first comprehensive and systematic survey on unified understanding of reaction and retrosynthesis prediction.