An explanation for high-frequency cycles of sea level in non-glacial times has remained elusive, despite more than two centuries of research since Lavoisier's seminal observations were published in 1789. In the development of seismic stratigraphy in the 1970s, putatively global high-frequency changes in relative sea level (Vail third-order cycles) were attributed to an unknown eustatic mechanism, prompting a search for Mesozoic ice ages. Over the last decade, a regional mechanism of sea-level control has been developed from studies of the sedimentary record in high-quality oil-industry data. These geological studies have supported the geophysical prediction that significant regional control of sea level is exercised by mantle-induced vertical motions of the Earth's surface. These vertical motions can occur over time intervals from several tens of million years to less than a million years, with amplitudes of tens of metres or more even at the shorter intervals. The vertical motions are not confined to regions with major hotspots. There are two related controls of surface vertical motion: evolution of mantle-convection cells, and pulsing flow within each cell. The effects are evident in the sedimentary record of North Atlantic basins. Mantle convection provides an alternative, regional, mechanism to eustatic control for explaining medium-frequency to high-frequency sea-level cycles.