I discuss several cases where a broken symmetry - either broken spontaneously or by construction - leads to ratcheting behavior in systems where dynamic boundaries interact with moving fluids.  Two examples feature reciprocal forcing combined with geometric anisotropy of boundaries.  In one case a solid body can be made to hover, and in another, a fluid is efficiently pumped.  I will also discuss the dynamics of a symmetric wing whose “forward flight” follows from a symmetry breaking instability, and how this dynamics is affected by the introduction of more biological realism.