Superfluidity is of tremendous interest in condensed matter physics and more recently, in engineering too. At non-zero temperatures, the superfluid and normal fluid interact with each other. After a brief introduction to the physics of the problem, we will consider a macro-scale and a micro-scale model, both of which describe the coupled dynamics of the two fluids. Mathematical analysis concerning the existence, regularity and uniqueness of solutions to these models will be presented. Among other things, the notion of weak-strong uniqueness will be relaxed to include “moderate” or less-regular strong solutions. All the results constitute joint work with Konstantina Trivisa (University of Maryland College Park).