Recent advance in imaging modalities used frequently in clinical routine can provide description of the geometrical and hemodynamical properties of the arterial tree in great detail. The combination of such information with models of blood flow of the arterial tree can provide further information, such as details in pressure and flow waves or details in the local flow field. Such knowledge maybe be critical in understanding the development or state of arterial disease and can help clinicians perform better diagnosis or plan better treatments. In the present review, the state of the art of arterial tree models is presented, ranging from 0-D lumped models, 1-D wave propagation model to more complex 3-D fluid-structure interaction models. Our development of a generic and patient-specific model of the human arterial tree permitting to study pressure and flow waves propagation in patients is presented. The predicted pressure and flow waveforms are in good agreement with the in vivo measurements. We discuss the utility of these models in different clinical application and future development of interest.