Nonlinear responses in the dynamics of climate system could be triggered by small change of forcing. Interactions between different components of Earth’s climate system are believed to cause abrupt and catastrophic transitions, of which anthropogenic forcing is a major and the most irreversible driver. Meantime, in the face of global climate change, extreme climatic events, such as extreme precipitations, heatwaves, droughts, etc., are projected to be more frequent, more intense, and longer in duration. These nonlinear responses in climate dynamics from tipping points to extreme events pose serious threats to human society on a large scale. Understanding the physical mechanisms behind them has potential to reduce related risks through different ways. The overarching objective of this dissertation is to quantify complex interactions, detect tipping points, and explore propagations of extreme events in the hydroclimate system from a new structure-based perspective, by integrating climate dynamics, causal inference, network theory, spectral analysis, and machine learning. More specifically, a network-based framework is developed to find responses of hydroclimate system to potential critical transitions in climate. Results show that system-based early warning signals towards tipping points can be located successfully, demonstrated by enhanced connections in the network topology. To further evaluate the long-term nonlinear interactions among the U.S. climate regions, causality inference is introduced and directed complex networks are constructed from climatology records over one century. Causality networks reveal that the Ohio valley region acts as a regional gateway and mediator to the moisture transport and thermal transfer in the U.S. Furthermore, it is found that cross-regional causality variability manifests intrinsic frequency ranging from interannual to interdecadal scales, and those frequencies are associated with the physics of climate oscillations. Besides the long-term climatology, this dissertation also aims to explore extreme events from the system-dynamic perspective, especially the contributions of human-induced activities to propagation of extreme heatwaves in the U.S. cities. Results suggest that there are long-range teleconnections among the U.S. cities and supernodes in heatwave spreading. Findings also confirm that anthropogenic activities contribute to extreme heatwaves by the fact that causality during heatwaves is positively associated with population in megacities.