Abstract The current power systems are undergoing a rapid transition towards their more active, flexible, and intelligent counterpart smart grid, which brings about tremendous challenges in many domains, e.g., integration of various distributed renewable energy sources, cyberspace security, demand-side management, and decision-making of system planning and operation. The fulfillment of advanced functionalities in the smart grid firmly relies on the underlying information and communication infrastructure, and the efficient handling of a massive amount of data generated from various sources, e.g., smart meters, phasor measurement units, and various forms of sensors. In this paper, a comprehensive survey of over 200 recent publications is conducted to review the state-of-the-art practices and proposals of machine learning techniques and discuss the trend in a wide range of smart grid application domains. This study demonstrates the increasing interest and rapid expansion in the use of machine learning techniques to successfully address the technical challenges of the smart grid from various aspects. It is also revealed that some issues still remain open and worth further research efforts, such as the high-performance data processing and analysis for intelligent decision-making in large-scale complex multi-energy systems, lightweight machine learning-based solutions, and so forth. Moreover, the future perspectives of utilizing advanced computing and communication technologies, e.g., edge computing, ubiquitous internet of things and 5G wireless networks, in the smart grid are also highlighted. To the best of our knowledge, this is the first review of machine learning-driven solutions covering almost all the smart grid application domains. Machine learning will be one of the major drivers of future smart electric power systems, and this study can provide a preliminary foundation for further exploration and development of related knowledge and insights.