The biochemical processes leading to the synthesis of new proteins are random, as they typically involve a small number of diffusing molecules. They lead to fluctuations in the number of proteins in a single cell as a function of time and to cell-to-cell variability of protein abundances. These in turn can lead to phenotypic heterogeneity in a population of genetically identical cells. Phenotypic heterogeneity may have important consequences for the development of multicellular organisms and the fitness of bacterial colonies, raising the question of how it is regulated. Here we review the experimental evidence that transcriptional regulation affects noise in gene expression, and discuss how the noise strength is encoded in the architecture of the promoter region. We discuss how models based on specific molecular mechanisms of gene regulation can make experimentally testable predictions for how changes to the promoter architecture are reflected in gene expression noise.