The oxygen-isotope records from Greenland ice cores show a very strong, reproducible pattern of alternation between warm Greenland Interstadials (GI) and cold Greenland Stadials (GS) at millennial-scale during the last glacial period. Here we summarise what is known about this variability from ice core records. The typical cycle has a sawtooth pattern, with a very rapid warming event (occurring in a few decades), a slow cooling trend, and then a final fast cooling. 25 such events have been numbered in the last glacial. The recent GICC05 age scale provides the best available age scale that can be directly applied to this stratigraphy, and we summarise the timing of the warming events, and the length and strength of each event. The Greenland stratigraphy can be transferred to other records if we make assumptions about the contemporaneous nature of rapid events in different archives. Other parameters, such as the snow accumulation rate, and the concentration of terrestrial dust and sea salt recorded in the Greenland cores, also show a strong contrasting pattern between GI and GS. Methane concentrations are generally high during GI and lower during GS, with the increase from GS to GI occurring within a century. Antarctic ice cores show a different pattern: each GI has an Antarctic counterpart, but Antarctica appears to warm while Greenland is in a GS, and cool during GI. These changes are consistent with a mechanism involving ocean heat transport, but the rapid nature of warmings poses a challenge for modellers, while the rapid methane changes pose questions about the pattern of land biosphere emissions during the glacial that are also relevant for understanding glacial-interglacial methane variability.