Both adaptive dynamic programming and other intelligent algorithms can solve the economic dispatch problem in the microgrid. Adaptive dynamic programming can reduce the computational burden, which the intelligent algorithms suffer from, by using function approximation structure to approximate performance index function. In recent years, it has been also widely used in economic dispatch in the microgrid. In this article, we introduce some recent research trends within the field of adaptive dynamic programming based economic dispatch. Adaptive dynamic programming is firstly reviewed. Then, the current research works about adaptive dynamic programming based economic dispatch are summarized and compared. Furthermore, we point out some topics for future studies.