Schools of fish, flocks of birds and other groups of organisms, can move in a highly coordinated fashion despite the fact that each member only experiences its immediate surroundings and there exists no obvious leader. Understanding how the global properties of the group, for example its shape, dynamics and organization, emerge from local interactions between individuals is a key goal of research in field of collective motion. The main theoretical tool used to investigate this is self-propelled particle (SPP) models. Over the past few decades development and analysis of SPP-models have provided us with considerable insight into how collective motion works in general, and in specific species of collectively moving animals. However, even simple SPP-models are often hard to analyze efficiently. Most often the only way to analyze them is by using computer simulations, and for more elaborate models even this approach may be unfeasible. This talk will contain a brief introduction to self-propelled particle models and an outline of why many of them are hard to analyze efficiently.