Micro-gyroscopes using micro-electro-mechanical system (MEMS) and micro-opto-electro-mechanical system (MOEMS) are the new-generation and recently well-developed gyroscopes produced by the combinations of the traditional gyroscope technology and MEMS/MOEMS technologies. According to the working principle and used materials, the newly-reported micro-gyroscopes in recent years include the silicon-based micromechanical vibratory gyroscope, hemispherical resonant gyroscope, piezoelectric vibratory gyroscope, suspended rotor gyroscope, microfluidic gyroscope, optical gyroscope, and atomic gyroscope. According to different sensitive structures, the silicon-based micromechanical vibratory gyroscope can also be divided into double frame type, tuning fork type, vibrating ring type, and nested ring type. For those micro-gyroscopes, in recent years, many emerging techniques are proposed and developed to enhance different aspects of performances, such as the sensitivity, angle random walk (ARW), bias instability (BI), and bandwidth. Therefore, this paper will firstly review the main performances and applications of those newly-developed MEMS/MOEMS gyroscopes, then comprehensively summarize and analyze the latest research progress of the micro-gyroscopes mentioned above, and finally discuss the future development trends of MEMS/MOEMS gyroscopes.