Equilibrium, traveling wave, and periodic orbit solutions of pipe and
plane Couette flow can now be computed precisely at Reynolds numbers
above the onset of turbulence. These invariant solutions capture the
complex dynamics of coherent roll-streak structures in wall-bounded
flows and provide a framework for connecting wall-bounded turbulence
to dynamical systems theory.  We present a number of newly computed
solutions of plane Couette flow and observe how they are visited by
the turbulent flow. What emerges is a picture of low-Reynolds
turbulence as a walk among a set of weakly unstable invariant
solutions.