Arterial hypertension affects one-quarter of the global population. It is the leading single contributor to global mortality and a major risk factor for a broad range of cardiovascular diseases, including stroke, myocardial infarction, heart failure, chronic kidney disease, peripheral vascular disease, cognitive decline, and premature death, to name just a few. The contents of this chapter are framed in the holistic fluid dynamics spirit of this book, with a focus on mathematical modelling and computation. The basics of hypertension, as found in most classical books or reviews, are briefly summarised, including definitions, prevalence, aetiology, and risk factors. We then examine associated cardiovascular changes, initially focusing on classical descriptions of events in the arterial side of the circulation, such as vascular remodelling and increased resistance. Next, we discuss the role of the venous system in arterial hypertension, starting with a description of the relevant properties of the venous district—such as its large proportion of total blood volume (between 70 and 85%) and its high compliance, particularly in the splanchnic region, which stores most of the blood. Reduced compliance of the venous system in arterial hypertension is then examined, beginning with the seminal works by London and Safar in the 1970s and 80s. Reduced venous compliance leads to the displacement of blood volumes from the peripheral venous system to the central circulation, causing disturbances in bodily fluid balance and an increase in blood pressure. The role of the sympathetic nervous system in regulating venous compliance is reviewed, including both clinical studies and recent experimental animal research. Finally, we briefly discuss some current theories on the aetiology of hypertension and highlight issues that warrant further investigation. The chapter concludes with a summary of key aspects in hypertension and recommendations for further reading.