The function of large arteries consists of dampening the pulsatile blood flow and pressure generated by the ventricular contraction to achieve a relatively steady flow in the peripheral circulation. Large arteries perform this function thanks to their elastic properties, which allow them to transfer part of the energy generated by the ventricles from systole to diastole. During systolic ejection, arteries accommodate part of the stroke volume through distension, thereby storing energy in the form of elastic energy. This energy is then used to push the blood forward in the circulation during diastole through elastic recoil. Arterial stiffening, as commonly observed with ageing and cardiovascular diseases, severely compromises this function, leading to an increased cardiac workload and enhanced transmission of pulsatility to peripheral organs. Indeed, an ever-growing body of evidence demonstrates the predictive value of larger artery stiffening for cardiovascular morbidity and mortality, as well as all-cause mortality. In this chapter, we first briefly introduce the concept of arterial stiffness and the similarities and differences between its many clinical declinations. In addition, we briefly review the history of pulse wave measurements, which constitute the foundation for the assessment of arterial stiffness and function. Then, we delve deeper into the role of arterial stiffness in the propagation and reflection of pulse waves in the circulation, also overviewing the detrimental effects of arterial stiffening for both the heart and peripheral organs. Furthermore, we introduce the pressure amplification phenomenon, the critical difference between central and peripheral (i.e. brachial) blood pressure, and how these may be altered by arterial stiffening. We then provide an overview of key metrics used in the clinic to quantify arterial stiffness. Notably, because many of these metrics are surrogates and not direct measures of arterial stiffness, we explain their relationship with arterial stiffness, focusing on their advantages and limitations in light of the available evidence of key literature studies. Finally, we conclude the chapter with a brief overview of arterial function assessment in today’s clinical practice and guidelines. We also highlight the future work needed for widespread clinical adoption of arterial stiffness measurements.