Flapping-wing vehicles， inspired by the wing kinematics of insects and birds， exhibit remarkable aerodynamic efficiency and maneuverability under low-Reynolds-number regimes. In contrast， flapping-wing rotor vehicles， an emerging research frontier in recent years， integrate passive rotational motion with flapping actuation， enabling enhanced hovering and vertical take-off/landing capabilities. It presents a systematic review of recent advancements in system modeling and control methodologies for flapping-wing micro air vehicles （FWMAVs） and flapping-wing rotor micro air vehicles （FWRMAVs）. It delves into the unsteady aerodynamic theories underlying the insect-inspired flapping-wing flight mechanism， and further explores the existing system modeling and control approaches tailored to insect-inspired FWMAVs and FWRMAVs. Finally， this review addresses current challenges in FWMAVs dynamics and control methodologies， including aerodynamic modeling of flexible wings and suppression of unsteady disturbances. It further highlights the insufficient research on flight dynamic characteristics and active attitude control of FWRMAVs， thereby outlining prospects for future investigations.