A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate in two different modes, namely, grid-connected and islanded modes. MGs face various challenges of voltage variations, frequency deviations, harmonics, unbalances, etc., due to the uncertain behavior of renewable sources. To study the impact of these issues, it is necessary to analyze the behavior of the MG system under normal and abnormal operating conditions. Two different tools are used for the analysis of microgrids under normal and abnormal conditions, namely, power flow and short-circuit analysis, respectively. Power flow analysis is used to determine the voltages, currents, and real and reactive power flow in the MG system under normal operating conditions. Short-circuit analysis is carried out to analyze the behavior of MGs under faulty conditions. In this paper, a review of power flow and short-circuit analysis algorithms for MG systems under two different modes of operation, grid-connected and islanded, is presented. This paper also presents a comparison of various power flow as well as short-circuit analysis techniques for MGs in tabular form. The modeling of different components of MGs is also discussed in this paper.