Cross-diffusion systems are non-linear parabolic systems describing the evolution of densities or concentrations of multicomponent populations in interaction. Namely in population dynamics, cross-diffusion systems play a key role in modelling the spatial segregation of competing species. In this talk we analyse the role of cross-diffusion terms in pattern formation and in the derivation of the cross-diffusion model, obtained as the singular limit of a parabolic system with linear diffusion and fast reaction. [1] Brocchieri, E., Corrias, L., Dietert, H. and Kim, Y-J. Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit, J. Math. Biol., 83 (2021). https://doi.org/10.1007/s00285-021-01679-y [2] N. Shigesada, K. Kawasaki, E. Teramoto. Spatial segregation of interacting species, J. Theor. Biol. 79.1 (1979): 83-99. https://www.sciencedirect.com/science/article/abs/pii/0022519379902583