Can we detect and describe the computational structure in dynamic processes and can we provide a quantitative characterization of essential aspects of this structure? When modeling for instance traffic in a city, the interactions between the individuals driving the cars, the bicycles, and pedestrians result in a dynamic self-organizing interaction structure, which is superimposed on the road network. This can be seen as a dynamical computational structure where information is exchanged, stored, and processed. What are the essential aspects of this structure, and how do they determine the way in which information is actually stored, transferred, and processed in complex systems? And what does that mean for the overall system behavior, that is, for their emergent properties? Can we then better understand emergent properties and critical phenomena such as tipping points? For instance, where do traffic jams come from, which all of sudden seem to appear from thin air? Or, can we get a deeper understanding of the systemic economic crises that struck us in 2008? Are we able to steer or control such emergent properties? What can we do to prevent traffic jams while maintaining the throughput on the road? Maybe by bringing down velocity, or slightly controlling the traffic entering a road on the individual car level? Or more dramatically, can we ‘nudge’ the behavior of countries, large companies, and/or individuals to fight the climate change? The ever increasing and abundant availability of data, both from science and society, drives our research. We study complex systems in the context of methods like multi-scale cellular automata, dynamic networks and individual agent based models. The challenges include data-driven modeling of multi-level systems and their dynamics as well as conceptual, theoretical and methodological foundations that are necessary to understand these processes and the associated predictability limits of such large-scale computer simulations.