Critical Infrastructure (CI) interdependencies have important consequences for crisis management, particularly when the crises are cross-border. However, research into CI interdependencies is still immature. The nature of large-scale, cross-border crises in these systems of systems is not easily understood. We have identified several aspects that need to be investigated to gain a more complete understanding of the development of crises in these systems. These aspects include the following: there is a need to understand CIs as interdependent elements of a complex system; ever-increasing interdependencies create new complexity; crises in CI are dynamically complex owing to the existence of significant time delays; there is a need for a long-term perspective; knowledge about CIs is fragmented and resides in many different stakeholders that need to be identified and brought together; there is a need for modelling techniques that can unite the fragmented CI knowledge; there is a need to create effective training and communication tools to transfer insights to crisis managers, policy makers and the general public.