Efficient methods for solving economic load dispatch (ELD) problems have been provided to build effective multi-objective evolutionary algorithms (MOEAs). ELD is a dynamic bi-objective optimization problem that is strictly limited. The MOEA applications to solve the ELD problems have been published in various publications since the 1990s. This paper explores the state of the art of this direction-related research. It addresses subjects such as standard MOEAs, traditional ELD problems, dynamic ELD problems, wind power integration ELD problems, electric car integration ELD problems and micro-grid ELD problems. Furthermore, several potential directions are also provided for future study.