Variability in induced pluripotent stem cell (iPSC) lines remains a concern for disease modeling and regenerative medicine. We have used RNA-sequencing analysis and linear mixed models to examine the sources of gene expression variability in 317 human iPSC lines from 101 individuals. We found that ∼50% of genome-wide expression variability is explained by variation across individuals and identified a set of expression quantitative trait loci that contribute to this variation. These analyses coupled with allele-specific expression show that iPSCs retain a donor-specific gene expression pattern. Network, pathway, and key driver analyses showed that Polycomb targets contribute significantly to the non-genetic variability seen within and across individuals, highlighting this chromatin regulator as a likely source of reprogramming-based variability. Our findings therefore shed light on variation between iPSC lines and illustrate the potential for our dataset and other similar large-scale analyses to identify underlying drivers relevant to iPSC applications.