Our study provides the highest resolution map to date of common regulatory variation in human PSCs. We show that variation in local gene regulation in iPSCs is similar to that in somatic tissues, with eQTLs driving cell-type specific expression profiles through distal tissue-specific regulatory elements. We have identified eQTLs that function primarily in pluripotent cells, a subset of which tag loci associated with disease. These loci may drive disease-susceptibility through molecular changes early in development or, more generally, in cells with ‘stem-like’ characteristics, which are not well captured by studies of differentiated primary tissues from adult individuals. A compelling example of this is the iPSC-specific eQTL regulating TERT expression. In human tissues, telomerase activity is mainly restricted to stem cells, with most somatic tissues silencing TERT expression. However, cancer cells bypass this tumour suppressive mechanism by reactivating telomerase activity47. This result highlights how iPSCs could be used to study the genetic effects of diseases that manifest in transient states during cellular growth and differentiation, including in cancer48.