In the first half of this talk, I will indicate a useful relationship between fluid (more precisely, Euler) flows on 3-manifolds and flows naturally associated to contact structures (Reeb flows). Using this relationship, I will show how to translate certain questions concerning fluid flows into the language of contact geometry. In the second part of the talk, I will describe relatively new techniques for studying Reeb flows. These techniques evolved out of Hofer's extension of "Gromov compactness" of holomorphic curves to certain symplectic manifolds with "non-bounded geometry."