Trait-associated genetic variants affect complex phenotypes primarily via regulatory mechanisms on the transcriptome. To investigate the genetics of gene expression, we performed cis- and trans-expression quantitative trait locus (eQTL) analyses using blood-derived expression from 31,684 individuals through the eQTLGen Consortium. We detected cis-eQTL for 88% of genes, and these were replicable in numerous tissues. Distal trans-eQTL (detected for 37% of 10,317 trait-associated variants tested) showed lower replication rates, partially due to low replication power and confounding by cell type composition. However, replication analyses in single-cell RNA-seq data prioritized intracellular trans-eQTL. Trans-eQTL exerted their effects via several mechanisms, primarily through regulation by transcription factors. Expression of 13% of the genes correlated with polygenic scores for 1,263 phenotypes, pinpointing potential drivers for those traits. In summary, this work represents a large eQTL resource, and its results serve as a starting point for in-depth interpretation of complex phenotypes.