The article discusses the Windkessel model, a simplified representation of the arterial system, which has been widely used to understand and study hemodynamics. The model, originally proposed by Frank, consists of two elements: resistance and compliance, which describe the decay of aortic pressure in diastole. However, this model falls short in explaining systolic pressure behavior. To address this limitation, the characteristic impedance was introduced as a third element, linking the lumped Windkessel to wave transmission phenomena. The three-element Windkessel model is used to estimate total arterial compliance from pressure and flow data, and it provides a more accurate description of the arterial system's behavior. The article also reviews various methods for estimating total arterial compliance, including the decay time method, the stroke volume over pulse pressure method, the area method, and the parameter estimation method. The Windkessel model is widely used in clinical studies, particularly in hypertension research, and has been applied to isolated hearts and artificial heart valve studies. Despite its limitations in modeling spatially distributed phenomena and wave travel, the Windkessel model remains a valuable tool for understanding and predicting arterial hemodynamics.The article discusses the Windkessel model, a simplified representation of the arterial system, which has been widely used to understand and study hemodynamics. The model, originally proposed by Frank, consists of two elements: resistance and compliance, which describe the decay of aortic pressure in diastole. However, this model falls short in explaining systolic pressure behavior. To address this limitation, the characteristic impedance was introduced as a third element, linking the lumped Windkessel to wave transmission phenomena. The three-element Windkessel model is used to estimate total arterial compliance from pressure and flow data, and it provides a more accurate description of the arterial system's behavior. The article also reviews various methods for estimating total arterial compliance, including the decay time method, the stroke volume over pulse pressure method, the area method, and the parameter estimation method. The Windkessel model is widely used in clinical studies, particularly in hypertension research, and has been applied to isolated hearts and artificial heart valve studies. Despite its limitations in modeling spatially distributed phenomena and wave travel, the Windkessel model remains a valuable tool for understanding and predicting arterial hemodynamics.