Community or modular structure is considered to be a significant property of large scale real-world graphs such as social or information networks. Detecting influential clusters or communities in these graphs is a problem of considerable interest as it often accounts for the functionality of the system. We aim to provide a thorough exposition of the topic, including the main elements of the problem, a brief introduction of the existing research for both disjoint and overlapping community search, the idea of influential communities, its implications and the current state of the art and finally provide some insight on possible directions for future research.