Dissipative phenomena are ubiquitous in physics, arising in systems across a vast range of energy scales, from condensed matter and fluid dynamics to astrophysics and cosmology. While traditional effective field theory (EFT) methods have been remarkably successful in describing isolated systems, many physically relevant systems involve interactions with environments that induce dissipation, noise, and non-conservative dynamics. Extending EFT techniques to such open systems has become an active and rapidly developing area of research. This thesis is devoted to the study of gravitational systems with dissipation and their field-theoretic description. In particular, it focuses on the following topics: an effective field theory description of dissipative effects in self-gravitating compact objects and their connection to gravitational-wave observations; models with dissipative dynamics in the evolution of the early and late-time universe in cosmology.