| Abstract :We shall survey recent progress in the treatment of Dirichlet, Neumann and transmission boundary value problems for the Stokes system of linear hydrostatics in Lipschitz domains. This program has been initiated in the 80's by Fabes, Kenig and Verchota who have developed a L^2-theory. Our goal is to essentially bring this program to completion by establishing optimal L^p-results. As a corollary, we are able to prove the well-posedness of the Poisson problem for the Stokes system in Sobolev-Besov spaces in Lipschitz domains. |