Some forms of the self-similar singularities for the Navier-Stokes equations have been ruled out, but there are still interesting scenarios which remain open. In the case of the Complex Ginzburg-Landau (CGL) equation one can get a fairly good (computational) picture about the situation concerning regularity and uniqueness, based on a combination of old and new results. Although the similarities between CGL and Navier-Stokes may admittedly not be very profound, one can hopefully still get useful insights from the CGL model.