Abstract: We consider scalar transport equations involving nonlocal interaction terms and different kinds of mobility and we present how to obtain weak solutions (in some regimes even entropy solutions) as many particle limit of a suitable nonlocal version of the deterministic follow-the-leader scheme, which can be interpreted as the discrete Lagrangian approximation of the target partial differential equation. We discuss both the cases of linear and nonlinear mobilities as well as how the evolution is affected when a diffusive term is taken into account. The content of this talk is based on several works obtained in collaborations with S. Daneri, M. Di Francesco, S. Fagioli, E. Runa and F. Stra.