Genetic regulation of gene expression is dynamic, as transcription can change during cell differentiation and across cell types. We mapped expression quantitative trait loci (eQTLs) throughout differentiation to elucidate the dynamics of genetic effects on cell type specific gene expression. We generated time-series RNA-sequencing data, capturing 16 time points from induced pluripotent stem cells to cardiomyocytes, in 19 human cell lines. We identified hundreds of dynamic eQTLs that change over time, with enrichment in enhancers of relevant cell types. We also found nonlinear dynamic eQTLs, which affect only intermediate stages of differentiation, and cannot be found by using data from mature tissues. These fleeting genetic associations with gene regulation may represent a new mechanism to explain complex traits and disease. We highlight one example of a nonlinear eQTL that is associated with body mass index.