Spatio-temporal action detection (STAD) aims to classify the actions present in a video and localize them in space and time. It has become a particularly active area of research in computer vision because of its explosively emerging real-world applications, such as autonomous driving, visual surveillance and entertainment. Many efforts have been devoted in recent years to build a robust and effective framework for STAD. This paper provides a comprehensive review of the state-of-the-art deep learning-based methods for STAD. First, a taxonomy is developed to organize these methods. Next, the linking algorithms, which aim to associate the frame- or clip-level detection results together to form action tubes, are reviewed. Then, the commonly used benchmark datasets and evaluation metrics are introduced, and the performance of state-of-the-art models is compared. At last, this paper is concluded, and a set of potential research directions of STAD are discussed.