This dissertation focuses on extreme behavior in complex adaptive networks and systems. A complex adaptive system (CAS) is a system in which a perfect understanding of the individual parts does not automatically convey a perfect understanding of the whole system's behavior. Its associated extreme behaviors (or events) are rare and violent phenomena that could be harmful to the major stakeholders in the system. In this work we investigated several aspects of extreme events in two typical CASs: a pro-IS online social network, and a Grand Canonical Minority Game (GCMG) system. Specifically, by applying analytical and modeling methods from a variety of domains (e.g., classical physics, game theory, graph theory, network analysis methods, statistics and probability theory), we provided both quantitative observations and theoretical explanations for various aspects of the systems, such as the roles played by different types of agents, the dynamics governing the evolution of groups in the pro-IS network, the impact of access to information on the power-law exponent, the temporal and inter-individual correlations of the agents, the mechanism for the generation of extreme events in the GCMG system, the temporal evolution of hierarchical network structures, the origin of polarizations, the systems' response to perturbations, the delays, etc. Our work not only provided theoretical explanations for those various observations, but also confirmed the intuition that the temporal and inter-individual correlations, non-stationarity, adaptation, single realization and an open boundary, etc. are common characteristics of a CAS that could be important for the existences of extreme events. This work may help pave the road for a more systematic and unified description of complex behaviors in different complex systems in the future.