The increasing number of small satellites has resulted in greater consideration of electric propulsion (EP) as potential thruster systems. Of these, ablative pulsed plasma thrusters (APPTs) are a type of EP system that is suitable for microsatellites. They have recently attracted attention for application in small satellites due to their simple and compact system. However, from a scientific perspective, we still have limited understanding regarding APPT mechanisms such as the acceleration mechanism, plasma propagation, and associated physical phenomena. From an engineering perspective, widespread adoption can be aided by the optimization of APPTs, including improvements in the thrust efficiency, energy bank miniaturization, and a better understanding of the plasma plume characteristics and possible interactions with spacecraft. These are some issues that still remain as challenges in the research and development of APPTs. This review discusses our current understanding of the fundamental mechanisms behind APPT operation as well as some new insights and recent progress associated with APPTs. Typical characterization methods for APPTs are presented along with discussion of the operation process and relevant physical phenomena. To support an engineering perspective, we also discuss optimization approaches for APPTs such as changes in the thruster geometry, alternative propellants, and electrical circuit optimization. New insights and novel approaches resulting from the use of modern technology in APPT research are also presented, along with current understanding that attempt to tie scientific perspectives with engineering observations, such as the physical reasons behind certain performance enhancements from optimization efforts. Finally, some remaining challenging issues are also discussed.