Genes interact in networks to orchestrate cellular processes. Here, we used coexpression networks based on natural variation in gene expression to study the functions and interactions of human genes. We asked how these networks change in response to stress. First, we studied human coexpression networks at baseline. We constructed networks by identifying correlations in expression levels of 8.9 million gene pairs in immortalized B cells from 295 individuals comprising three independent samples. The resulting networks allowed us to infer interactions between biological processes. We used the network to predict the functions of poorly-characterized human genes, and provided some experimental support. Examining genes implicated in disease, we found that IFIH1, a diabetes susceptibility gene, interacts with YES1, which affects glucose transport. Genes predisposing to the same diseases are clustered non-randomly in the network, suggesting that the network may be used to identify candidate genes that influence disease susceptibility. These analyses showed that human coexpression networks based on natural variation may offer information on gene functions and interactions. We then examined the extent to which networks change upon stress. We studied changes in expression levels and gene relationships induced by two stresses: endoplasmic reticulum (ER) stress and exposure to ionizing radiation (IR). Using large datasets, we found between 30-70% of genes change expression upon stress. In contrast, the majority (between 65-95%) of gene relationships are maintained as assessed using statistical, network and machine learning methods. However, a subset of genes altered relationships upon stress. These genes tended to be critical for the cellular response to the specific stress examined. For example, BIP and CHOP altered relationships in ER stress; p21, GADD45A and CCNB1 altered relationships in IR stress. Some genes with altered relationships have not been implicated in ER or IR stress or do not change expression; these are genes that may be critical but remain unexplored. We provide evidence implicating two such genes, INHBE and SLC3A2, in the response to ionizing radiation. Our results suggest that the majority of gene relationships are maintained upon stress, but those genes with altered relationships tend to be critical to the stress response.