Technical Abstract: Catastrophic events share characteristic nonlinear behaviors that are often generated by cross-scale interactions and feedbacks among system elements. These events result in surprises that cannot be easily predicted based on information obtained at a single scale. Progress to date on catastrophic events has focused on one of two areas: (1) nonlinear dynamics through time without an explicit consideration of spatial connectivity, and (2) spatial connectivity and the spread of contagious processes without a consideration of cross-scale interactions and feedbacks. These approaches have rarely ventured beyond traditional disciplinary boundaries. We provide an interdisciplinary, conceptual, and general mathematical framework for understanding and forecasting nonlinear dynamics through time and across space. We illustrate the generality and utility of our approach using new data and a recasting of published data from ecology (wildfires, desertification), epidemiology (infectious diseases) and engineering (structural failures). We show that decisions minimizing the likelihood of catastrophic events must be based on cross-scale interactions and such decisions will often be counter-intuitive. Given the continuing challenges associated with global change, approaches that cross disciplinary boundaries, to include interactions and feedbacks at multiple scales, are needed to increase our ability to predict catastrophic events and to develop strategies for minimizing their occurrence and impacts. Our framework is an important step in developing predictive tools and designing new experiments to examine cross-scale interactions.