Induced pluripotent stem cell (iPSC) technology has enormous potential to provide improved cellular models of human disease. However, variable genetic and phenotypic characterisation of many existing iPSC lines limits their potential use for research and therapy. Here, we describe the systematic generation, genotyping and phenotyping of 711 iPSC lines derived from 301 healthy individuals by the Human Induced Pluripotent Stem Cells Initiative (HipSci: http://www.hipsci.org). Our study outlines the major sources of genetic and phenotypic variation in iPSCs and establishes their suitability as models of complex human traits and cancer. Through genome-wide profiling we find that 5-46% of the variation in different iPSC phenotypes, including differentiation capacity and cellular morphology, arises from differences between individuals. Additionally, we assess the phenotypic consequences of rare, genomic copy number mutations that are repeatedly observed in iPSC reprogramming and present a comprehensive map of common regulatory variants affecting the transcriptome of human pluripotent cells.