Changes in sea level (relative to the moving crust) are associated with changes in ocean volume (mostly thermal expansion) and in ocean mass (melting and continental storage): zeta(t) = zeta(steric)(t) + zeta(eustatic)(t). Recent compilations of global ocean temperatures by Levitus and coworkers are in accord with coupled ocean/atmosphere modeling of greenhouse warming; they yield an increase in 20th century ocean heat content by 2 x 10(23) J (compared to 0.1 x 10(23) J of atmospheric storage), which corresponds to zeta(greenhouse)(2000) = 3 cm. The greenhouse-related rate is accelerating, with a present value zeta(greenhouse)(2000) approximately 6 cm/century. Tide records going back to the 19th century show no measurable acceleration throughout the late 19th and first half of the 20th century; we take zeta(historic) = 18 cm/century. The Intergovernmental Panel on Climate Change attributes about 6 cm/century to melting and other eustatic processes, leaving a residual of 12 cm of 20th century rise to be accounted for. The Levitus compilation has virtually foreclosed the attribution of the residual rise to ocean warming (notwithstanding our ignorance of the abyssal and Southern Oceans): the historic rise started too early, has too linear a trend, and is too large. Melting of polar ice sheets at the upper limit of the Intergovernmental Panel on Climate Change estimates could close the gap, but severe limits are imposed by the observed perturbations in Earth rotation. Among possible resolutions of the enigma are: a substantial reduction from traditional estimates (including ours) of 1.5-2 mm/y global sea level rise; a substantial increase in the estimates of 20th century ocean heat storage; and a substantial change in the interpretation of the astronomic record.