This talk focuses on scaling limits for interacting particle systems, evolving according to an energy-conservative dynamics. In a general context, one of the ultimate goals of statistical mechanics is to derive the macroscopic evolution of energy from a microscopic dynamics given by a chain of coupled oscillators. This is expected to hold through a diffusive space-time scaling limit. For the sake of clarity I will focus on one specific model, involving harmonic oscillators perturbed by a stochastic noise, provided with random i.i.d. masses. I will investigate the macroscopic behavior of this system under two different aspects: first, the hydrodynamic equations, and second, the macroscopic fluctuations of energy.