With the fast development of various positioning techniques such as Global Position System (GPS), mobile devices and remote sensing, spatio-temporal data has become increasingly available nowadays. Mining valuable knowledge from spatio-temporal data is critically important to many real-world applications including human mobility understanding, smart transportation, urban planning, public safety, health care and environmental management. As the number, volume and resolution of spatio-temporal data increase rapidly, traditional data mining methods, especially statistics-based methods for dealing with such data are becoming overwhelmed. Recently deep learning models such as recurrent neural network (RNN) and convolutional neural network (CNN) have achieved remarkable success in many domains due to the powerful ability in automatic feature representation learning, and are also widely applied in various spatio-temporal data mining (STDM) tasks such as predictive learning, anomaly detection and classification. In this paper, we provide a comprehensive review of recent progress in applying deep learning techniques for STDM. We first categorize the spatio-temporal data into five different types, and then briefly introduce the deep learning models that are widely used in STDM. Next, we classify existing literature based on the types of spatio-temporal data, the data mining tasks, and the deep learning models, followed by the applications of deep learning for STDM in different domains including transportation, on-demand service, climate & weather analysis, human mobility, location-based social network, crime analysis, and neuroscience. Finally, we conclude the limitations of current research and point out future research directions.