Certain classes of non-local pseudo-differential operators can be associated with Markov processes and this result has an infinite dimensional counterpart too. The best known example is the Levy process with its generator an integro-differential operator. In this talk we will give an introduction to stochastic Navier-Stokes equation with jump (Levy) noise and point out opportunities for harmonic as well as stochastic analysis to gain understanding in solvability theory and applications such as control and filtering theory.