In recent years, conservation laws with space-dependent nonlocal fluxes have attracted growing attention due to their wide range of applications in fluid mechanics, including granular flow, sedimentation, aggregation phenomena, crowd dynamics, and, in particular, traffic flow, which serves as the main motivating example of this talk.

We provide an introduction to nonlocal conservation laws, where nonlocality is modeled through a spatial convolution operator. We discuss key analytical properties of these models, including the uniqueness of weak solutions and the singular limit as the convolution kernel converges to a Dirac delta.

Furthermore, we present a general framework for the numerical approximation of such equations and highlight possible extensions of both the theory and the numerical methods, as well as remaining open problems in the literature.