The variability of the Antarctic and Greenland ice sheets occurs on various timescales and is important for projections of sea level rise; however, there are substantial uncertainties concerning future ice-sheet mass changes. In this Review, we explore the degree to which short-term fluctuations and extreme glaciological events reflect the ice sheets’ long-term evolution and response to ongoing climate change. Short-term (decadal or shorter) variations in atmospheric or oceanic conditions can trigger amplifying feedbacks that increase the sensitivity of ice sheets to climate change. For example, variability in ocean-induced and atmosphere-induced melting can trigger ice thinning, retreat and/or collapse of ice shelves, grounding-line retreat, and ice flow acceleration. The Antarctic Ice Sheet is especially prone to increased melting and ice sheet collapse from warm ocean currents, which could be accentuated with increased climate variability. In Greenland both high and low melt anomalies have been observed since 2012, highlighting the influence of increased interannual climate variability on extreme glaciological events and ice sheet evolution. Failing to adequately account for such variability can result in biased projections of multi-decadal ice mass loss. Therefore, future research should aim to improve climate and ocean observations and models, and develop sophisticated ice sheet models that are directly constrained by observational records and can capture ice dynamical changes across various timescales.