Gene expression varies across cells in a population or a tissue. This heterogeneity has come into sharp focus in recent years through developments in new imaging and sequencing technologies. However, our ability to measure variation has outpaced our ability to interpret it. Much of the variability may arise from random effects occurring in the processes of gene expression (transcription, RNA processing and decay, translation). The molecular basis of these effects is largely unknown. Likewise, a functional role of this variability in growth, differentiation and disease has only been elucidated in a few cases. In this review, we highlight recent experimental and theoretical advances for measuring and analyzing stochastic variation.