Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and biological networks. In this paper, we introduce fundamental concepts and unique properties of adaptive networks through a brief, non-comprehensive review of recent literature on mathematical/computational modeling and analysis of such networks. We also report our recent work on several applications of computational adaptive network modeling and analysis to real-world problems, including temporal development of search and rescue operational networks, automated rule discovery from empirical network evolution data, and cultural integration in corporate merger.