Why do societies collapse? Some famous examples include: Easter Island, the Maya, the Roman Empire and Chinese dynasties. I have developed mathematical models for these cases and will present what these models teach us. I will also provide a general perspective of the methodology I employed in modelling past cases of collapse. The modelling does not focus on the collapse in particular, but rather on the long-term development of a society from its beginning to end. To build an accurate model we need to identify the relevant feedback mechanisms that operate over those time scales. In the case of societies, the long-term feedback loops involve its complexity and resource usage. What is complexity? That's a key topic that will be addressed in the talk.