How do the choices made by individual pedestrians influence the large-scale crowd dynamics?
What are the factors that slow them down and motivate them to seek detours?
What happens when multiple crowds pursuing different targets interact with each other?

We will consider how the answers to these questions shape a class of popular PDE-based models. This talk is meant to be self-contained and our focus will be on the internal consistency of such models rather than the details of their numerical implementation. I will emphasize the role of anisotropy, the geometric intuition behind our choice of optimal directions, and connections to the non-zero-sum game theory. (Joint work with Elliot Cartee.)