In recent times, with the increase in the penetration of various renewable energy sources (RESs) into power systems, the complications related to the stability issues have increased. The main contribution of this paper is an in‐depth analysis of research in microgrid based on small‐signal, transient, and voltage stability. The small‐signal stability has been discussed based on uncertain load, limitation in power generation capacity, and nature of sluggish feedback observed in few microgrid systems. Instability caused by a transient phenomenon in microgrid has been thoroughly analyzed for losses in distributed energy resources (DERs), islanding and transition modes of operation, load shedding, and faults causing instability. The voltage fluctuations are duly considered in the perspective of load shedding, type of loads, power unbalancing, and different types of faults in microgrid systems. The existing controllers have been compared based on steady‐state error, response time, and robustness etc. The voltage, frequency, and active/reactive power control are analyzed based on centralized, decentralized, hierarchal/distributed control schemes aiming stabilization of microgrid systems. Finally, stability improvement features have been explored in detail, finding the implementation of microgrid stabilizers, energy storage devices, FACTS devices, load balancing, resource forecasting including the adaptive controller. Hence, the uniqueness of this paper can be considered as a state‐of‐the‐art review of the abovementioned stability components in the microgrid system which is not available in the published literature with a similar amount of vastness.