One of the problems that are associated to power systems is islanding condition, which must be rapidly and properly detected to prevent any negative consequences on the system's protection, stability, and security. This paper offers a thorough overview of several islanding detection strategies, which are divided into two categories: classic approaches, including local and remote approaches, and modern techniques, including techniques based on signal processing and computational intelligence. Additionally, each approach is compared and assessed based on several factors, including implementation costs, non-detected zones, declining power quality, and response times using the analytical hierarchy process (AHP). The multi-criteria decision-making analysis shows that the overall weight of passive methods (24.7%), active methods (7.8%), hybrid methods (5.6%), remote methods (14.5%), signal processing-based methods (26.6%), and computational intelligent-based methods (20.8%) based on the comparison of all criteria together. Thus, it can be seen from the total weight that hybrid approaches are the least suitable to be chosen, while signal processing-based methods are the most appropriate islanding detection method to be selected and implemented in power system with respect to the aforementioned factors. Using Expert Choice software, the proposed hierarchy model is studied and examined.