Quantum many body systems driven out-of-equilibrium by means of time-dependent Hamiltonians are currently of great interest both theoretically and experimentally. In this talk the quantum Ising model with a periodic modulation of the transverse magnetic field is considered and its dynamical properties are investigated under different driving conditions. The Ising model is the simplest many body system exhibiting a second order quantum phase transition at the critical value of the transverse field h=h_c, where both magnetic observables, and other physical quantities that are not observables in the quantum-mechanical sense, exhibit scaling relations: the transverse magnetic susceptibility, the concurrence, the fidelity susceptibility all display finite-size scaling according to the exponents belonging to the Ising universality class at criticality. We address the question of the validity of these scaling relations when the system is periodically driven across the critical point. Furthermore, the asymptotic steady state Entanglement Entropy is investigated, showing that it approaches a volume law.