Systems with strongly interacting constituents can acquire macroscopic coherence and develop collective excitations at new energy scales that would be difficult to foresee from the microscopic ingredients. Bose-Einstein condensation and superconductivity are two paradigmatic examples of this kind of emergence. In this thesis I consider how these phenomena change in the presence of a cavity, broadly construed as some kind of field that is capable of mediating long-range forces across the system. I focus specifically on two examples: a kind of polariton in which strongly-interacting excitons on a lattice couple to photon field in a physical cavity, and forms a supersolid state in which the condensate coexists with spatial order; and superconductivity in strontium titanate, considered as a case in which the collective motions of the electron fluid and the lattice, respectively plasmons and optic phonons, hybridize to produce superconductivity mediated by long-range forces.