The basic elements of probabilistic seismic-hazard analysis (psha) were established almost four decades ago and psha has now become the most widely used approach for estimating seismic-design loads. Although the use of psha is widespread, considerable confusion remains regarding the details of how the calculations should be performed. This situation is largely a result of the way the discipline of psha evolved through a series of articles, reports, and software packages. This article demonstrates that the feature of psha about which there is perhaps the greatest degree of misunderstanding is the treatment of the aleatory variability in ground- motion prediction equations, which exerts a very pronounced influence on the calculated hazard. Probabilistic hazard studies performed in recent years have frequently resulted in appreciably higher design ground motions than had been obtained in previous assessments carried out in the 1970s and 1980s, often sparking controversial debate. Although several factors may contribute to the higher estimates of seismic hazard in modern studies, the main reason for these increases is that in the earlier studies the ground-motion variability was either completely neglected or treated in a way that artificially reduced its influence on the hazard estimates.