Dramatic changes in the dynamics of complex systems occur with significant consequences. Such an unexpected change is usually undesirable and notably difficult to predict since models of complex systems are usually not accurate enough to predict reliably where and when critical thresholds may occur. Examples of these phenomena include, but are not limited to, flutter instabilities in aeroelastic systems, traffic congestion in transportation systems, regime shifts in ecological systems, and disease outbreaks in epidemiological systems. By combining nonlinear dynamics with data-driven methods, we develop innovative mechanistic data-driven approaches capable of predicting these catastrophic events and their impacts on the dynamics of complex systems. Our developed methods dramatically minimizes the effort required for a comprehensive analysis, monitoring, and design of complex dynamical systems susceptible to instabilities.