The accelerated electrification of transport systems with EVs has brought new challenges for charging scheduling, fleet management, and charging infrastructure location and configuration planning. In this review, we have provided a systematic review of the recent development in strategic, tactical, and operational decisions for demand responsive transport system planning using electric vehicles (EV-DRT). We have summarized recent developments in mathematical modeling approaches by focusing on the problems of dynamic EV-DRT optimization, fleet sizing, and charging infrastructure planning. A list of existing open-access datasets, numerical test instances, and software are provided for future research in EV-DRT and related problems. Current research gaps are identified and future research directions are discussed.