Network community structure is one of the most fundamental and important topological properties of complex networks, within which the links between nodes are very dense, but between which they are quite sparse. Network clustering algorithms which aim to discover all natural network communities from given complex networks are fundamentally important for both theoretical researches and practical applications, and can be used to analyze the topological structures, understand the functions, recognize the hidden patterns, and predict the behaviors of complex networks including social networks, biological networks, World Wide Webs and so on. This paper reviews the background, the motivation, the state of arts as well as the main issues of existing works related to discovering network communities, and tries to draw a comprehensive and clear outline for this new and active research area. This work is hopefully beneficial to the researchers from the communities of complex network analysis, data mining, intelligent Web and bioinformatics.