This paper introduces recent advances on flapping-wing Micro and Nano Aerial Vehicles (MAVs and NAVs) based on Piezoelectric Actuators (PEA). Therefore, this work provides essential information to address the development of such bio-inspired aerial robots. PEA are commonly used in micro-robotics and precise positioning applications (e.g., micro-positioning and micro-manipulation), whereas within the Unmanned Aerial Vehicles (UAVs) domain, motors are the classical actuators used for rotary or fixed-wing configurations. Therefore, we consider it pertinent to provide essential information regarding the modeling and control of piezoelectric cantilever actuators to accelerate early design and development stages of aerial microrobots based on flapping-wing systems. In addition, the equations describing the aerodynamic behavior of a flapping-wing configuration are presented.