In this talk, we review how the topological Reidemeister torsion of a manifold can be recovered from the data of the gradient flowlines and periodic orbits of a dynamical system given by a circle-valued Morse function. If time permits, we will discuss possible connections with Seiberg-Witten invariants, implicit in the work of Taubes and Meng. This talk is of an expository nature, with an aim towards introducing the work of Hutchings and Lee.