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Understanding the principles of geophysical phenomena is an essential and challenging task. "Model-driven" approaches have supported the development of geophysics for a long time; however, such methods suffer from the curse of dimensionality and may inaccurately model the subsurface. "Data-driven" techniques may overcome these issues with increasingly available geophysical data. In this article, we review the basic concepts of and recent advances in data-driven approaches from dictionary learning to deep learning in a variety of geophysical scenarios. Explorational geophysics including data processing, inversion and interpretation will be mainly focused. Artificial intelligence applications on geoscience involving deep Earth, earthquake, water resource, atmospheric science, satellite remoe sensing and space sciences are also reviewed. We present a coding tutorial and a summary of tips for beginners and interested geophysical readers to rapidly explore deep learning. Some 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 activate learning.