Flapping-wing rotor (FWR) is an innovative bio-inspired micro aerial vehicle capable of vertical take-off and landing. This unique design combines active flapping motion and passive wing rotation around a vertical central shaft to enhance aerodynamic performance. The research on FWR, though relatively new, has contributed to 6% of core journal publications in the micro aerial vehicle field over the past two decades. This paper presents the first comprehensive review of FWR, analysing the current state of the art, key advances, challenges, and future research directions. The review highlights FWR’s distinctive kinematics and aerodynamic superiority compared to traditional flapping wings, fixed wings, and rotary wings, discussing recent breakthroughs in efficient, passive wing pitching and asymmetric stroke amplitude for lift enhancement. Recent experiments and remote-controlled take-off and hovering tests of single and dual-motor FWR models have showcased their effectiveness. The review compares FWR flight performance with well-developed insect-like flapping-wing micro aerial vehicles as the technology readiness level progresses from laboratory to outdoor flight testing, advancing from the initial flight of a 2.6 g prototype to the current free flight of a 60-gram model. The review also presents ongoing research in bionic flexible wing structures, flight stability and control, and transitioning between hovering and cruise flight modes for an FWR, setting the stage for potential applications.