Manifolds with the homology of S1xS3 have been a topic of increased interest in the last few years. In this talk I will discuss my work (in progress) to construct a monopole Floer theoretic invariant of homology S1xS3's that is the analog of a Heegaard Floer invariant defined by Levine-Ruberman, and is expected to be related to the Seiberg-Witten theoretic Casson-type invariant of Mrowka-Ruberman-Saveliev. I will discuss these and other invariants briefly to give context for my construction.