We discuss uid structure interaction for exterior ows, for Reynolds numbers ranging from about one to several thousand. New applications demand a better quantitative understanding of the details of such ows, and this has stimulated a revival of interest in this topic. Astonishingly, in spite of the apparent simplicity of low Reynolds number ows, their precise prediction turns out to be numerically demanding even with today's computers. On the basis of simple examples we review the progress that has been made over the recent years in the analysis of such problems through a combined use of techniques from asymptotic analysis, symbolic computation, and computational uid dynamics, and discuss open problems which one should be able to solve with the techniques presented here.