This paper describes the state of development for false‐twist texturing of thermoplastic continuous filament yarns. Supply yarn parameters are shown to significantly affect the textured product. Quantitative and qualitative information is given to describe these effects. The thermodynamic and crystallization rate parameters are presented for nylon 6, nylon 66, and polyethylene‐terepthalate. Equations are given for calculation of temperature‐time profiles in yarns during texturing. Both the fundamentals of twisting using spindle or friction twisters are summarized. The effect of process variables on twist distribution and crimp rigidity are presented. Finally, experiments are described which show how force‐elongation curves for textured nylon 6 can be made similar to nylon 66. Recommendations for future work are discussed. Ways are needed to improve the dye uniformity and reduce barré from textured yarns in piece‐dyed fabrics. More information should be reported on the effect of processing constants (tension and temperature gradients) on crystallization rate phenomena and structural changes during texturing. Basic information on the effect of yarn and process constants on friction twisting with the many commercial units needs reported. The final goal of this fundamental work should be a mathematical model, which rigorously describes the texturing process. With this model, yarn and machinery manufacturers could optimize their products more fully for the use of the texturing mills.