Micro-electromechanical systems (MEMS) vibrating gyroscopes have gained a lot of attention over the last two decades because of their low power consumption, easy integration, and low fabrication cost. The usage of the gyroscope equipped with an inertial measurement unit has increased tremendously, with applications ranging from household devices to smart electronics to military equipment. However, reliability issues are still a concern when operating this inertial sensor in harsh environments, such as to control the movement and alignment of mini-satellites in space, tracking firefighters at an elevated temperature, and assisting aircraft navigation in gusty turbulent air. This review paper focuses on the key fundamentals of the MEMS vibrating gyroscopes, first discussing popular designs including the tuning fork, gimbal, vibrating ring, and multi-axis gyroscopes. It further investigates how bias stability, angle random walk, scale factor, and other performance parameters are affected in harsh environments and then discusses the reliability issues of the gyroscopes.