Dynamic earth models are used to better understand the impact of mantle dynamics on the vertical motion of continents and regional and global sea level change since the Late Cretaceous. A hybrid approach combines inverse and forward models of mantle convection and accounts for the principal contributors to long-term sea level change: the evolving distribution of ocean floor age, dynamic topography in oceanic and continental regions, and the geoid. We infer the relative importance of dynamic versus other factors of sea level change, determine time-dependent patterns of dynamic subsidence and uplift of continents, and derive a sea level curve. We find that both dynamic factors and the evolving distribution of sea floor age are important in controlling sea level. We track the movement of continents over large-scale dynamic topography by consistently mapping between mantle and plate frames of reference, and we find that this movement results in dynamic subsidence and uplift of continents. The amplitude of dynamic topography in continental regions is larger than global sea level in several regions and periods, so that it has controlled regional sea level in North and South America and Australia since the Late Cretaceous, northern Africa and Arabia since the late Eocene, and Southeast Asia in the Oligocene-Miocene. Eastern and southern Africa have experienced dynamic uplift over the last 20 to 30 m.y., whereas Siberia and Australia have experienced Cenozoic tilting. The dominant factor controlling global sea level is a changing oceanic lithosphere production that has resulted in a large amplitude sea level fall since the Late Cretaceous, with dynamic topography offsetting this fall.