With dramatic development of artificial intelligence in recent years, energy management based on “learning to optimize” is regarded as a promising research direction of smart grid. The designs of existing learning-based energy management approaches are quite different and there is no doubt that understanding the advantages and limitations of these ideas is essential to capture the research trends in this field. In this survey, references are carefully selected and categorized into three main groups: Optimal solution learning, warm-start learning, and constraints learning. The design details and advantages of these groups are systematically analyzed. Further, based on the shortcomings of existing studies, we propose five major challenges and provided some potential solutions. We hope this survey can provide more comprehensive information and new perspectives for researchers in this field.