The ureter and its peristalsis motions have long been of significant interest in biomechanics. In this article we review experimental, theoretical, and numerical studies of the behavior of the ureter together with its mechanical properties, emphasizing studies that contain information of importance in building a virtual simulation tool of the complete ureter that includes its complex geometry, nonlinear material properties, and interaction with urine flow. A new technique to model the contraction of a ureter, which directly applies wall forces to model pacemaker activities, is presented. The required further steps to capture the full complex movement of the peristalsis are discussed, aiming to construct a computational platform that will provide a reliable tool to assist in the investigation and design of material devices (stents) for the renal system.