In a smart grid environment, advanced metering infrastructure (AMI) and intelligent sensors have been deployed extensively. As a result, large-scale and fine-grained smart grid data are more convenient to be collected, in which outliers exist pervasively, caused by system failures, environmental effects, and human interventions. Outlier deletion is always implemented in data preprocessing for improving data quality. However, due to the fact that real records that reflect rare and unusual patterns are also recognized as outliers, outlier mining is necessary to be carried out with the aim of discovering knowledge on abnormal patterns in power generation, transmission, distribution, transformation, and consumption. To the best of our knowledge, a comprehensive and systematic review of outlier data treatment methods is still lacked in the smart grid environment. We, in this paper, aim at presenting the review of outlier data treatment methods toward smart grid applications and categorize them into outlier rejection and outlier mining groups. Since we do this survey from the perspective of data-driven analytics and data mining methods, information security technologies are barely discussed in this paper. Based on a general overview of outlier data treatment methods, we make the contribution of providing the application scenarios of outlier rejection and outlier mining in the smart grid environment. With the construction of smart grid throughout the world, dealing with outlier data has become more crucial for the security and reliability of power system operation. Therefore, we also discuss some future challenges of outlier data treatment toward smart energy management.