Insular electricity grids are considered to have a more fragile structure than the mainland ones due to several factors such as the lower inertia because of lower number of generation facilities connected to the system, absence or insufficient interconnection with the main grid, etc. The recent trend of integrating large portions of environmentally sustainable power generation units that have a significantly volatile nature in the generation mix (such as wind and solar energy conversion systems) within this fragile structure, poses profound challenges that need deeper and specific analysis. This study aims to provide an overview of insular power system structures and operational requirements, especially under increasing penetration of renewable energy sources. Firstly, a general evaluation of insular power systems is presented. Then, potential challenges are thoroughly discussed together with opportunities to tackle them. Future technological developments, as well as innovative applications are also given special attention. Hence, this paper contributes to the scarce literature regarding insular power systems by providing a critical overview of issues regarding their operation and possible solutions.