Starting from A. Turing's work on diffusion-driven instability", I shall first explain how diffusion has been used in modeling various biological/chemical pattern formation -- from hydra's regeneration phenomenon to the recent CIMA chemical reaction. Then, I will discuss the inability of diffusion to help create patterns in the classical Lotka-Volterra competition model and thereby introduce the notion of cross-diffusion. Using such a system, I shall discuss what cross-diffusion is capable of creating.