My research looks at the physics of collective behavior and emergent properties in real-world systems which are 'complex': from the physical, biological, medical domains through to social and even financial domains. A complex system is one in which unexpected phenomena emerge spontaneously at the macro-level, through the micro-level interactions of many objects over time. For example, traffic jams arise from the interactions of cars -- but understanding what a single car can do tells us little about the jams that emerge. The same holds true for applications in medicine (cancer tumors), molecular biology (macroscopic chromosone dynamics within E. Coli), neurology (brain function from individual neuron firings) through to economics and sociology (mass downloads of a given YouTube video, or crashes in financial markets). The fascinating feature of Complex Systems is that they all contain many interacting objects, with strong feedback from both inside and outside the system, and are typically far from equilibrium and exhibit extreme behavior.