In this talk, we'll present our results about invariant Gibbs measures for the periodic nonlinear Schrödinger equation (NLS) in 2D, for any (defocusing and renormalized) odd power nonlinearity, and for cubic NLW in 3D. This is joint work with Bjoern Bringmann (IAS), Yu Deng (USC) and Andrea Nahmod (UMass Amherst).