Recent advances in machine learning have significantly influenced the simulation of Newtonian fluids, and there is growing interest in extending these techniques to complex fluids with non-Newtonian properties, such as viscoelastic flows. In this talk, we present data-driven frameworks for constructing interpretable reduced-order models of viscoelastic fluids, combining both linear and nonlinear dimensionality reduction methods with the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm. In particular, we explore the development of physics-informed metrics to enhance nonlinear dimensionality reduction tailored to viscoelastic behavior. We also highlight recent progress in the SciML domain, with a focus on applications to droplet dynamics.