Human pluripotent cells such as human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) and their in vitro differentiation models hold great promise for regenerative medicine as they provide both a model for investigating mechanisms underlying human development and disease and a potential source of replacement cells in cellular transplantation approaches. The remarkable developmental plasticity of pluripotent cells is reflected in their unique chromatin marking and organization patterns, or epigenomes. Pluripotent cell epigenomes must organize genetic information in a way that is compatible with both the maintenance of self-renewal programs and the retention of multilineage differentiation potential. In this review, we give a brief overview of the recent technological advances in genomics that are allowing scientists to characterize and compare epigenomes of different cell types at an unprecedented scale and resolution. We then discuss how utilizing these technologies for studies of hESCs has demonstrated that certain chromatin features, including bivalent promoters, poised enhancers, and unique DNA modification patterns, are particularly pervasive in hESCs compared with differentiated cell types. We outline these unique characteristics and discuss the extent to which they are recapitulated in iPSCs. Finally, we envision broad applications of epigenomics in characterizing the quality and differentiation potential of individual pluripotent lines, and we discuss how epigenomic profiling of regulatory elements in hESCs, iPSCs and their derivatives can improve our understanding of complex human diseases and their underlying genetic variants.