The increasingly common disappearance of glaciers is striking, and it is often used to highlight the effects of anthropogenic climate change to the public. This approach is more effective when modern glacier and climate change is placed within a frame of reference. Here we present a new, efficient method to assess the timing of glacier birth and death. We model equilibrium line altitudes (ELAs) of 22 Icelandic glaciers through time, and in doing so produce the first regional estimates of glacier lifespans. We force the model with three Holocene temperature reconstructions and five future-climate projections, while also exploring the effects of glacial-isostatic adjustment and variable precipitation. Mass balance parameters are tuned for each ice cap using modern data. Geologically-constrained inception ages are used to validate individual simulations. The timing of Icelandic glacier inception likely ranged from before the Holocene to as late as the Little Ice Age. Anthropogenic warming is expected to cut short the lifespans of glaciers that have existed for thousands of years. By quantifying the controlling factors we show that topography and the rate of summer temperature change are the primary controls of glacier lifespans in Iceland. Topography, represented by the difference between the modern ELA and the highest local topography, is ten-times as important as ELA sensitivity to temperature. This easy-to-measure topographic metric exerts a first-order control on the timing of inception and the future loss of accumulation area and it can be used to contextualize ongoing glacier disappearance.