We examine some issues related to shape optimization of fluid flows.We begin by providing some simple examples of computational resultsfor such problems. We then examine, using the simple setting ofincompressible flow in a channel, some difficulties that arise in the numerical computation of shape optimization problems and oftechniques for overcoming these difficulties. We close with a briefdiscussion of the analysis of shape optimization problems forNavier-Stokes flows, focusing on existence questions and thederivation of optimality systems and formulas for the shape gradientof the cost functional.