Photons coupled to atomic Rydberg states form Rydberg polaritons that exhibit properties of both light and strongly-interacting matter. I will describe experiments characterizing Rydberg polaritons in an optical cavity in which we observe strong polariton-polariton interactions through antibunching of light. In separate experiments, we show that degenerate optical cavities with a nonplanar geometry induce effective magnetic fields for photons, resulting in Landau levels. Combining strongly interacting Rydberg polaritons with photonic Landau levels provides a promising route toward realizing Laughlin states of light. In the second part of my talk, I will describe proposed experiments investigating the  transport properties of strongly interacting atomic Fermi gases. Both Rydberg polaritons and atomic fermions provide platforms for observing the novel properties of strongly interacting quantum systems driven out of equilibrium.