In this talk I will present some results obtained for the unitary dynamics of the Ising spin chain after a quantum quench. I will first explain how one can access the dynamics of this and similar integrable models. Then, focusing in particular on two-time correlation functions, I will discuss the behavior of different observables, the role of the integrals of motion and of the initial condition. I will also present different ways to test the equilibration properties of the system. \ \ noindent Refs: L. Foini, L. F. Cugliandolo, A. Gambassi, Phys. Rev. B 84, 212404 (2011); J. Stat. Mech. (2012) P09011.