Microgrids, as localized and flexible power systems capable of operating in both grid-connected and islanded modes, have introduced significant challenges in traditional power system analysis due to the high penetration of Distributed Energy Resources (DERs). These challenges particularly relate to short-circuit current (SCC) calculation and relay protection (RP) coordination, where conventional methods often fail to account for bidirectional power flows, inverter-based resources, and dynamic topologies. This paper presents a review of existing approaches to short-circuit analysis and relay protection coordination in microgrids. Through a critical examination of recent literature and practical implementations, we identify the current gaps and limitations in prevailing methodologies. Based on this review, the most promising methods for short-circuit calculation and relay protection coordination are selected and subjected to an in-depth analysis. These methods are applied and evaluated on a real-life microgrid system using ETAP (Electrical Transient Analyzer Program). Simulation results and performance assessments are presented, highlighting the strengths and weaknesses of the selected approaches. The findings provide valuable insights into current limitations and offer concrete directions for future research and development in the domain of microgrid protection and reliability.