Communities, also called clusters or modules, are groups of nodes which probably share common properties and/or play similar roles within a graph. They widely exist in real networks such as biological, social, and information networks. Allowing users to interactively browse and explore the community structure, which is essential for understanding complex systems, is a challenging yet important research topic. My work has been focused on visualization approaches to exploring the community structure in graphs based on automatic community detection results.In this dissertation, we first report a formal user study that investigated the essential influence factors, benefits, and constraints of a community based graph visualization system in a background application of seeking information from text corpora. A general evaluation methodology for exploratory visualization systems has been proposed and practiced. The evaluation methodology integrates detailed cognitive load analysis and users' prior knowledge evaluation with quantitative and qualitative measures, so that in-depth insights can be gained. The study revealed that visual exploration based on the community structure benefits the understanding of real networks. A literature review and a set of interviews were then conducted to learn tasks facing such graph exploration and the state-of-the-arts. This work led to community related graph visualization task taxonomy. Our examination of existing graph visualization systems revealed that a large number of community related graph visualization tasks are poorly supported in existing approaches. To bridge the gap, several novel visualization techniques are proposed. In these approaches, graph topology information is mapped to a multidimensional space where the relationships between the communities and the nodes can be explicitly explored. Several user studies and case studies have been conducted to demonstrate the usefulness of these systems in real-world applications.