A micro-opto-electro-mechanical system (MOEMS) accelerometer features high precision, electromagnetic interference resistance, good adaptability to the environment, high reliability, and easy miniaturization, which is the major development trend of inertial instruments. According to the optical measurement principle, this paper divides MOEMS accelerometers into three categories, which are based on the direct intensity modulation (IM), the undulatory property of light, and the light-matter interaction separately. Following a brief introduction to the measurement principles and typical cases, we systematically analyze the merits and demerits of the three accelerometers, as well as their potential application scenarios. Given the research progress in MOEMS accelerometers, we also present their development tendencies.