Microgrids that are integrated with distributed energy resources (DERs) provide many benefits, including high power quality, energy efficiency and low carbon emissions, to the power grid. Microgrids are operated either in grid-connected or island modes running on different strategies. However, one of the major technical issues in a microgrid is unintentional islanding, where failure to trip the microgrid may lead to serious consequences in terms of protection, security, voltage and frequency stability, and safety. Therefore, fast and efficient islanding detection is necessary for reliable microgrid operations. This paper provides an overview of microgrid islanding detection methods, which are classified as local and remote. Various detection methods in each class are studied, and the advantages and disadvantages of each method are discussed based on performance evaluation indices such as non-detection zone (NDZ), detection time, error detection ratio, power quality and effectiveness in multiple inverter cases. Recent modifications on islanding methods using signal processing techniques and intelligent classifiers are also discussed. Modified passive methods with signal processing and intelligent classifiers are addressing the drawbacks of passive methods and are getting more attention in the recently published works. This comprehensive review of islanding methods will provide power utilities and researchers a reference and guideline to select the best islanding detection method based on their effectiveness and economic feasibility.