While traditional means of influencing material properties are static, I will present our recent studies of dynamical control of high-temperature superconductors via light pulses. Specifically, I will discuss both light enhanced superconductivity, for which we propose a parametric amplification mechanism, as well as light induced superconductivity. As a second platform, I will describe dynamics in driven cavity-BEC systems. These systems feature a competition of Bose condensation and density wave order, resulting in a superradiant phase transition. Motivated by the challenges of light induced superconductivity, we demonstrate dynamical control of the superradiant transition of a cavity-BEC system via periodic driving of the pump laser. We show that the dominant density wave order of the superradiant state can be suppressed, and that the subdominant competing order of Bose-Einstein condensation emerges in the steady state. This establishes a foundational principle of dynamical control of competing orders analogous to a hypothesized mechanism for light induced superconductivity. Furthermore, we show that additional, non-equilibrium density wave orders, which do not exist in equilibrium, can be stabilized dynamically, and finally, that for strong driving chaotic dynamics emerges. Time permitting, I will present a recent project on the generalization of path integrals and its application to second sound of Bose Einstein condensates.