The major cause of sea-level change during ice ages is the exchange of water between ice and ocean and the planet’s dynamic response to the changing surface load. Inversion of ∼1,000 observations for the past 35,000 y from localities far from former ice margins has provided new constraints on the fluctuation of ice volume in this interval. Key results are: (i) a rapid final fall in global sea level of ∼40 m in <2,000 y at the onset of the glacial maximum ∼30,000 y before present (30 ka BP); (ii) a slow fall to −134 m from 29 to 21 ka BP with a maximum grounded ice volume of ∼52 × 10⁶ km³ greater than today; (iii) after an initial short duration rapid rise and a short interval of near-constant sea level, the main phase of deglaciation occurred from ∼16.5 ka BP to ∼8.2 ka BP at an average rate of rise of 12 m⋅ka⁻¹ punctuated by periods of greater, particularly at 14.5–14.0 ka BP at ≥40 mm⋅y⁻¹ (MWP-1A), and lesser, from 12.5 to 11.5 ka BP (Younger Dryas), rates; (iv) no evidence for a global MWP-1B event at ∼11.3 ka BP; and (v) a progressive decrease in the rate of rise from 8.2 ka to ∼2.5 ka BP, after which ocean volumes remained nearly constant until the renewed sea-level rise at 100–150 y ago, with no evidence of oscillations exceeding ∼15–20 cm in time intervals ≥200 y from 6 to 0.15 ka BP. Significance Several areas of earth science require knowledge of the fluctuations in sea level and ice volume through glacial cycles. These include understanding past ice sheets and providing boundary conditions for paleoclimate models, calibrating marine-sediment isotopic records, and providing the background signal for evaluating anthropogenic contributions to sea level. From ∼1,000 observations of sea level, allowing for isostatic and tectonic contributions, we have quantified the rise and fall in global ocean and ice volumes for the past 35,000 years. Of particular note is that during the ∼6,000 y up to the start of the recent rise ∼100−150 y ago, there is no evidence for global oscillations in sea level on time scales exceeding ∼200 y duration or 15−20 cm amplitude.

Using glacial rebound models we have inverted observations of crustal rebound and shoreline locations to estimate the ice thickness for the major glaciations over northern Eurasia and to predict the palaeo‐topography from late MIS‐6 (the Late Saalian at c. 140 kyr BP) to MIS‐4e (early Middle Weichselian at c. 64 kyr BP). During the Late Saalian, the ice extended across northern Europe and Russia with a broad dome centred from the Kara Sea to Karelia that reached a maximum thickness of c. 4500 m and ice surface elevation of c. 3500 m above sea level. A secondary dome occurred over Finland with ice thickness and surface elevation of 4000 m and 3000 m, respectively. When ice retreat commenced, and before the onset of the warm phase of the early Eemian, extensive marine flooding occurred from the Atlantic to the Urals and, once the ice retreated from the Urals, to the Taymyr Peninsula. The Baltic‐White Sea connection is predicted to have closed at about 129 kyr BP, although large areas of arctic Russia remained submerged until the end of the Eemian. During the stadials (MIS‐5d, 5b, 4) the maximum ice was centred over the Kara‐Barents Seas with a thickness not exceeding c. 1200 m. Ice‐dammed lakes and the elevations of sills are predicted for the major glacial phases and used to test the ice models. Large lakes are predicted for west Siberia at the end of the Saalian and during MIS‐5d, 5b and 4, with the lake levels, margin locations and outlets depending inter alia on ice thickness and isostatic adjustment. During the Saalian and MIS‐5d, 5b these lakes overflowed through the Turgay pass into the Aral Sea, but during MIS‐4 the overflow is predicted to have occurred north of the Urals. West of the Urals the palaeo‐lake predictions are strongly controlled by whether the Kara Ice Sheet dammed the White Sea. If it did, then the lake levels are controlled by the topography of the Dvina basin with overflow directed into the Kama‐Volga river system. Comparisons of predicted with observed MIS‐5b lake levels of Komi Lake favour models in which the White Sea was in contact with the Barents Sea.