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The smart grid is enabling the collection of massive amounts of high-dimensional and multi-type data about the electric power grid operations, by integrating advanced metering infrastructure, control technologies, and communication technologies. However, the traditional modeling, optimization, and control technologies have many limitations in processing the data; thus, the applications of artificial intelligence (AI) techniques in the smart grid are becoming more apparent. This survey presents a structured review of the existing research into some common AI techniques applied to load forecasting, power grid stability assessment, faults detection, and security problems in the smart grid and power systems. It also provides further research challenges for applying AI technologies to realize truly smart grid systems. Finally, this survey presents opportunities of applying AI to smart grid problems. The paper concludes that the applications of AI techniques can enhance and improve the reliability and resilience of smart grid systems.