In this talk, I will consider a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system, which arises in population dynamics. This system has entropy dissipation properties on which one can rely to design a robust and convergent numerical scheme for its numerical simulation. In terms of numerical analysis, I will present discrete compactness techniques, entropy-dissipation estimates and a new adaptation of the so-called duality estimates for parabolic equations in Laplacian form. I will also present numerical experiments illustrating the influence of the nonlocality in the system: on convergence properties, as an approximation of the local system and on the development of diffusive instabilities. This is a joint work with Antoine Zurek (UTC).