In this talk we give an overview on some basic probabilistic methods and questions in the study of the local and long time dynamics of nonlinear PDE and show how certain well-posedness results that are not available using only deterministic techniques (eg. Fourier and harmonic analysis) can be obtained when introducing randomization in the set of initial data and using powerful but still classical tools from probability as well. We focus on 3 prototypes: i) Probabilistic well posedness for periodic nonlinear Schr"odinger equation; ii) probabilistic well posedness for derivative nonlinear wave equation with null form on $\mathbb R^2$ and iii) long time solutions to some fluid equations (periodic): Navier-Stokes and modified surface quasigeostrophic equation.