The arterial Windkessel is a simplified model of the arterial system that describes its hemodynamics using resistance and compliance. Frank's original two-element Windkessel model, which includes resistance and compliance, was later improved by introducing characteristic impedance as a third element. This third element links the Windkessel model to transmission phenomena such as wave travel. The Windkessel model is used to estimate total arterial compliance from pressure and flow data and to describe the input impedance of the arterial system with physiologically interpretable parameters. However, it is a lumped model and thus not suitable for assessing spatially distributed phenomena or wave travel aspects. The three-element Windkessel model, which includes resistance, compliance, and characteristic impedance, provides a more accurate description of the arterial system, particularly in terms of pressure-flow relations throughout the cardiac cycle. The four-element Windkessel model further includes inertance, which accounts for the inertial properties of the arterial system. The Windkessel model has various clinical applications, including the assessment of cardiac output, peripheral resistance, and arterial compliance. It is also used in the study of ventriculo-arterial coupling and in the evaluation of arterial stiffness. The model has been shown to be useful in predicting cardiovascular morbidity and mortality, and it has been applied in various studies to assess the effects of changes in arterial compliance and peripheral resistance. Despite its limitations, the Windkessel model remains a valuable tool in the study of arterial hemodynamics and cardiovascular physiology.The arterial Windkessel is a simplified model of the arterial system that describes its hemodynamics using resistance and compliance. Frank's original two-element Windkessel model, which includes resistance and compliance, was later improved by introducing characteristic impedance as a third element. This third element links the Windkessel model to transmission phenomena such as wave travel. The Windkessel model is used to estimate total arterial compliance from pressure and flow data and to describe the input impedance of the arterial system with physiologically interpretable parameters. However, it is a lumped model and thus not suitable for assessing spatially distributed phenomena or wave travel aspects. The three-element Windkessel model, which includes resistance, compliance, and characteristic impedance, provides a more accurate description of the arterial system, particularly in terms of pressure-flow relations throughout the cardiac cycle. The four-element Windkessel model further includes inertance, which accounts for the inertial properties of the arterial system. The Windkessel model has various clinical applications, including the assessment of cardiac output, peripheral resistance, and arterial compliance. It is also used in the study of ventriculo-arterial coupling and in the evaluation of arterial stiffness. The model has been shown to be useful in predicting cardiovascular morbidity and mortality, and it has been applied in various studies to assess the effects of changes in arterial compliance and peripheral resistance. Despite its limitations, the Windkessel model remains a valuable tool in the study of arterial hemodynamics and cardiovascular physiology.