In this talk, we will discuss the dynamics on Teichmuller space and moduli space of square-tiled surfaces. For square-tiled surfaces, one can explicitly write down the SL(2,R)-orbit on the moduli space. To study the dynamics of Teichmueller flow of the SL(2,R)-action, we study its derivative, namely the Kontsevich--Zorich cocycle (KZ cocycle). In this talk, we will define what a KZ cocycle is, and by following explicit examples, we will show how one can compute the Kontsevich--Zorich monodromy. Time permitting, we will also compute the Lyapunov spectrum of the Kontsevich--Zorich cocycle for some square-tiled surfaces.