Extreme events are an emergent property of many complex, nonlinear systems in which various interdependent components and their interaction lead to a competition between organized (interaction dominated) and irregular (fluctuation dominated) behavior. Recent advances in nonlinear dynamics and complexity science provide a new approach to the understanding and modeling of extreme events and natural hazards. The main connection of extreme events to nonlinear dynamics arises from the recognition that they are not isolable phenomena but must be understood in terms of interactions among different components, within and outside the specific system. A wide range of techniques and approaches of complexity science are directly relevant to geosciences, e.g., nonlinear modeling and prediction, state space reconstruction, statistical self-similarity and its dynamical origins, stochastic cascade models, fractals and multifractals, network theory, self-organized criticality, etc. The scaling of processes in geosciences has been one of the most active areas of studies and has the potential to provide better tools for risk assessment and analysis. Many studies of extreme events in geosciences are also contributing to the basic understanding of their inherent properties, e.g., maximum entropy production and criticality, space-time cascades, and fractional Lévy processes. The need for better data for extreme events is evident in the necessity for detailed statistical analysis, e.g., in marine storms, nonlinear correlations, etc. The Chapman Conference on Complexity and Extreme Events held (2010) in Hyderabad, India, was focused on the understanding of natural hazards mainly from the perspective of complexity science. The emerging theme from the conference was the recognition of complexity science as the interdisciplinary framework for the understanding of extreme events and natural hazards.