Fracton phases are characterized by their elementary excitations having restricted mobility, and have recently been of relevance in several subjects, from quantum information to thermalization, from gravity to elasticity. In the context of hydrodynamics it has been shown theoretically, and confirmed experimentally, that such restricted mobility leads to novel emergent scaling laws. In this talk, I will introduce a framework to describe the hydrodynamics of fractons and predict such scaling laws, with particular focus on systems with conserved dipole and momentum. This hydrodynamics turns out to have rather exotic properties, owing to the fact that dipole conservation leads to a non-trivial extension of spacetime symmetries. After developing an effective theory approach that allows accounting for fluctuations, I will show that such theory contains relevant nonlinearities that lead to the emergence of stochastic non-Gaussian universality classes, even in three spatial dimensions, thus constituting a breakdown of its local hydrodynamic description.