The use of tissue engineering to regenerate viable tissue relies on selecting the appropriate cell line, developing a resorbable scaffold and optimizing the culture conditions including the use of biomolecular cues and sometimes mechanical stimulation. This review of the literature focuses on the required scaffold properties, including the polymer material, the structural design, the total porosity, pore size distribution, mechanical performance, physical integrity in multiphase structures as well as surface morphology, rate of resorption and biocompatibility. The chapter will explain the unique advantages of using textile technologies for tissue engineering scaffold fabrication, and will delineate the differences in design, fabrication and performance of woven, warp and weft knitted, braided, nonwoven and electrospun scaffolds. In addition, it will explain how different types of tissues can be regenerated by each textile technology for a particular clinical application. The use of different synthetic and natural resorbable polymer fibers will be discussed, as well as the need for specialized finishing techniques such as heat setting, cross linking, coating and impregnation, depending on the tissue engineering application.