Are human societies dynamical systems? Can they be studied—and, perhaps, to a degree predicted—with the methods of complexity science, such as agent-based models and big data analytics? If yes, what are the limits to prediction? A particularly challenging question is, can we forecast the dynamics of societal resilience and its obverse, sociopolitical unrest or even breakdown? So far efforts to predict onset of rebellions and civil wars using theory-free big data approaches have proved unsuccessful. An alternative approach, based on Structural-Demographic Theory (SDT), which integrates mechanism-based models with data and focuses on the dynamics of structural drivers for instability over the long-term (thus, requiring a historical approach), has shown better promise. Specifically, several recent studies utilizing the SDT framework have proven adept at predicting (or “retrodicting”) sociopolitical instability in c.20 past societies. It was also used in 2010 to successfully forecast outbreak of US instability 10 years in the future (in 2020). Collectively, this work is producing a growing body of evidence showcasing the ability of SDT-based approaches to uncover critical societal dynamics in the deep past as well as more contemporary cases. The next step in these efforts is to employ these insights towards the future. Here, we outline the SDT approach and document how it can be employed to explore the dynamics of any number of past and contemporary societies, appealing to researchers to pursue this line of research in as many cases as possible. The overall goal of this research is to empirically test SDT in a most rigorous way, using it to forecast coming periods of unrest. Because the theory is likely to fail in many ways, the second goal is to learn from these errors so that we can further refine the theory (or develop better-working alternatives). Specifically, we will learn: (1) how accurately (if at all) does the SDT framework predict future levels of sociopolitical instability (integrating incidence of antigovernment demonstrations, violent riots, and armed conflict); (2) What are the relative contributions of possible drivers of instability, including those proposed by SDT, as well as other theories, in explaining instability levels; and (3) are there key ‘leverage points’ that might help mitigate the negative consequences of instability?