Pressures in the hydrospheres of large ocean worlds extend to ranges exceeding those in Earth deepest oceans. In this regime, dense water ices and other high-pressure phases become thermodynamically stable and can influence planetary processes at a global scale. The presence of high-pressure ices sets large icy worlds apart from other smaller water-rich worlds and complicates their study. Here we provide an overview of the unique physical states, thermodynamics, dynamic regimes, and evolution scenarios specific to large ocean worlds where high-pressure ice polymorphs form. We start by (i) describing the current state of knowledge for the interior states of large icy worlds in our solar system (i.e. Ganymede, Titan and Callisto). Then we (ii) discuss the thermodynamic and physical specifics of the relevant high–pressure materials, including ices, aqueous fluids and hydrates. While doing this we (iii) describe the current state of the art in modeling and understanding the dynamic regimes of high-pressure ice mantles. Based on these considerations we (iv) explore the different evolution scenarios for large icy worlds in our solar system. We (v) conclude by discussing the implications of what we know on chemical transport from the silicate core, extrapolation to exoplanetary candidate ocean worlds, limitations to habitability, differentiation diversity, and perspectives for future space exploration missions and experimental measurements.knowledge for the interior states of large icy worlds in our solar system (i.e. Ganymede, Titan and Callisto). Then we (ii) discuss the thermodynamic and physical specifics of the relevant high–pressure materials, including ices, aqueous fluids and hydrates. While doing this we (iii) describe the current state of the art in modeling and nderstanding the dynamic regimes of high-pressure ice mantles. Based on these considerations we (iv) explore the different evolution scenarios for large icy worlds in our solar system. We (v) conclude by discussing the implications of what we know on chemical transport from the silicate core, extrapolation to exoplanetary candidate ocean worlds, limitations to habitability, differentiation diversity, and perspectives for future space exploration missions and experimental measurements.