Genetic effects on gene expression and splicing can be modulated by cellular and environmental factors; yet interactions between genotypes, cell type, and treatment have not been comprehensively studied together. We used an induced pluripotent stem cell system to study multiple cell types derived from the same individuals and exposed them to a large panel of treatments. Cellular responses involved different genes and pathways for gene expression and splicing and were highly variable across contexts. For thousands of genes, we identified variable allelic expression across contexts and characterized different types of gene-environment interactions, many of which are associated with complex traits. Promoter functional and evolutionary features distinguished genes with elevated allelic imbalance mean and variance. On average, half of the genes with dynamic regulatory interactions were missed by large eQTL mapping studies, indicating the importance of exploring multiple treatments to reveal previously unrecognized regulatory loci that may be important for disease.