“Model-driven” and “data-driven” approaches together have helped humans understand the principles of geophysical phenomena for a long time. With increasingly available geophysical data, a new data-driven technique, i.e., deep learning, has played an important role in the accurate prediction of complex system states and relieving the curse of dimensionality in large temporal and spatial geophysical applications. In this article, we review the basic concepts of and recent advances in data-driven deep learning approaches in a variety of geophysical scenarios. Explorational geophysics including data processing and imaging, are the main focus. Deep learning applications in the geosciences including the Earth interior, earthquakes, water resources, atmospheric science, satellite remote sensing, and space sciences are also reviewed. A coding tutorial and a summary of tips for rapidly exploring deep learning are presented for beginners and interested readers of geophysics. Several promising directions are provided for future research involving deep learning in geophysics, such as unsupervised learning, transfer learning, multimodal deep learning, federated learning, uncertainty estimation, and active learning.