The increased penetration of distributed generation (DG), renewable energy utilization, and the introduction of the microgrid concept have changed the shape of conventional electric power networks. Most of the new power system networks are transforming into the DG model integrated with renewable and non-renewable energy resources by forming a microgrid. Islanding detection in DG systems is a challenging issue that causes several protection and safety problems. A microgrid operates in the grid-connected or stand-alone mode. In the grid-connected mode, the main utility network is responsible for a smooth operation in coordination with the protection and control units, while in the stand-alone mode, the microgrid operates as an independent power island that is electrically separated from the main utility network. Fast islanding detection is, therefore, necessary for efficient and reliable microgrid operations. Many islanding detection methods (IdMs) are proposed in the literature, and each of them claims better reliability and high accuracy. This study describes a comprehensive review of various IdMs in terms of their merits, viability, effectiveness, and feasibility. The IdMs are extensively analysed by providing a fair comparison from different aspects. Moreover, a fair analysis of a feasible and economical solution in view of the recent research trend is presented.