The microscopic nature of dark matter remains a major outstanding question in particle physics and cosmology, and many simple models are now in tension with experimental constraints such as direct detection bounds. In this talk, I will introduce the notion of “gapped continuum” in quantum field theories, and explain how it can be realized explicitly by a field propagating on a 5D warped space background with a soft wall. I will then describe how to calculate cross sections and decay rates involving gapped continuum states, as well as study their equilibrium and non-equilibrium thermodynamics. With this theoretical framework in hand, I will present a fully realistic model of dark matter consisting of gapped continuum states, interacting with the Standard Model via the Z portal. Direct detection bounds, which normally rule out Z portal interactions for thermal-relic dark matter, are avoided due to a strong suppression of the relevant cross sections by a mechanism peculiar to gapped continuum. Some interesting and potentially testable predictions of this model, such as continuous decays of the dark matter states throughout the history of the universe, as well as striking collider signatures, will also be discussed.