Several congenital and acquired conditions may result in severe narrowing of the urethra in men, which represent an ongoing surgical challenge and a significant burden on both health and quality of life. In the field of urethral reconstruction, tissue engineering has emerged as a promising alternative to overcome some of the limitations associated with autologous tissue grafts. In this direction, preclinical as well as clinical studies, have shown that degradable scaffolds are able to restore the normal urethral architecture, supporting neo-vascularization and stratification of the tissue. While a wide variety of degradable biomaterials are under scrutiny, such as decellularized matrices, natural, and synthetic polymers, the search for scaffold materials that could fulfill the clinical performance requirements continues. In this article, we discuss the design requirements of the scaffold that appear to be crucial to better resemble the structural, physical, and biological properties of the native urethra and are expected to support an adequate recovery of the urethral function. In this context, we review the biological performance of the degradable polymers currently applied for urethral reconstruction and outline the perspectives on novel functional polymers, which could find application in the design of customized urethral constructs.