  The seemingly simple problem of determining the drag on a body moving through
a very viscous fluid has, for over 150 years, been a source of theoretical
confusion, mathematical paradoxes, and experimental artifacts, primarily
arising from the complex boundary layer structure of the flow near the body and
at infinity. We review the extensive experimental and theoretical literature on
this problem, with special emphasis on the logical relationship between
different approaches. The survey begins with the developments of matched
asymptotic expansions, and concludes with a discussion of perturbative
renormalization group techniques, adapted from quantum field theory to
differential equations. The renormalization group calculations lead to a new
prediction for the drag coefficient, one which can both reproduce and surpass
the results of matched asymptotics.
