The idea that aging is largely the result of (endogenous) stress appears to be at odds with the concept of biological 'clocks', which seem to programme and terminate cellular aging processes. Here, data are reviewed that show that telomeres, the major clock identified in human cells so far, do in fact measure stress and damage accumulation much more than simple mitotic time. Telomere shortening is significantly stress-dependent due to a telomere-specific damage repair deficiency. This identifies telomere-driven human cell replicative senescence as a stress response with high potential importance for human aging.