Cohesin is a well-known mediator of sister chromatid cohesion, but it also influences gene expression and development. These non-canonical roles of cohesin are not well understood, but are vital: gene expression and development are altered by modest changes in cohesin function that do not disrupt chromatid cohesion. To clarify cohesin's roles in transcription, we measured how cohesin controls RNA polymerase II (Pol II) activity by genome-wide chromatin immunoprecipitation and precision global run-on sequencing. On average, cohesin-binding genes have more transcriptionally active Pol II and promoter-proximal Pol II pausing than non-binding genes, and are more efficient, producing higher steady state levels of mRNA per transcribing Pol II complex. Cohesin depletion frequently decreases gene body transcription but increases pausing at cohesin-binding genes, indicating that cohesin often facilitates transition of paused Pol II to elongation. In many cases, this likely reflects a role for cohesin in transcriptional enhancer function. Strikingly, more than 95% of predicted extragenic enhancers bind cohesin, and cohesin depletion can reduce their association with Pol II, indicating that cohesin facilitates enhancer-promoter contact. Cohesin depletion decreases the levels of transcriptionally engaged Pol II at the promoters of most genes that don't bind cohesin, suggesting that cohesin controls expression of one or more broadly acting general transcription factors. The multiple transcriptional roles of cohesin revealed by these studies likely underlie the growth and developmental deficits caused by minor changes in cohesin activity.