With the accelerating electrification of public transit systems, the number of electric buses (EBs) in China has increased substantially. The operation management of EBs is of great significance for reducing the carbon emissions of the public transit system. Herein, we firstly introduce the development history of EBs in China and Western countries, and summarize the existing issues in the EB operation management in practice. Then a framework of EB operation management is proposed, and current studies are summarized from the perspectives of energy consumption estimation, vehicle scheduling, energy-efficient driving, resource allocation and benefit evaluation. We point out the techniques and methods down the road on EB operation management. Finally, the challenges are systematically summarized. We conclude that the future works that need to be focused on include: electric bus network planning, battery life estimation based on actual data, intelligent scheduling, and adoption of new power supply and charging modes.