In this talk, I will present our theoretical and computational approaches to describe excited-states in quantum matter, and predicting emergent states created by external drives. Understanding the role of such light-matter interactions in the regime of correlated electronic systems is of paramount importance to fields of study across condensed matter physics and ultrafast dynamics. With our approaches we can access correlated electron-photon and photon-phonon dynamics, essential to our latest work on driving quantum systems far out-of-equilibrium to control the coupled electronic and vibrational degrees-of-freedom. I will present our ideas on predicting transient correlations in quantum matter where key questions remain on the underlying excitation mechanisms, as well as on how to optimize and stabilize such short-lived electronic phases. In the second part of my talk, I will demonstrate how to generalize these approaches in the context of cavity control of quantum matter and quantum transduction.