Abstract: Several open problems in cosmology — including the nature of inflation, dark matter, and dark energy — involve spacetime-filling media with unknown microphysics, and can be probed so far only through their gravitational effects. This observation motivates a systematic open-system approach, in which gravity evolves in the presence of a generic, unobservable environment. In this talk, I will present a general framework for open gravitational dynamics based on General Relativity and the Schwinger-Keldysh formalism. As an application, I will describe the most general conservative and dissipative dynamics of scalar and tensor perturbations during single-clock inflation. I will conclude by discussing future prospects for dissipative dark sectors in the late universe.