Many group activities can be represented as a complex network where entities (vertices) are connected in pairs by lines (edges). Uncovering a useful global structure of complex networks is important for understanding system behaviors and in providing global guidance for application designs. We briefly review existing network models, discuss several tools used in the traditional graph theory, distributed computing, distributed systems, and social network communities, and point out their limitations. We discuss opportunities to uncover the structural properties of complex networks, especially in a mobile environment, and we summarize three promising approaches for uncovering useful structures: trimming, layering, and remapping. Finally, we present some challenges in algorithmic techniques, with a focus on distributed and localized solutions, to represent various structures.