The development of electronic textiles used for wearable devices and systems for healthcare monitoring applications has experienced rapid growth in the last decade. Knowledge and understanding of the textile structural hierarchy, as well as the ability to define properties from the fiber and yarn to the fabric level are crucial to the selection of materials and design and performance of wearable systems. However, few studies have approached the selection of optimal e-textile structures with respect to material, electrical, and signal performance properties of sensors used for long-term biological signal monitoring. In this work, a review of e-textile structural properties (fiber, yarn, and fabric) for electrocardiogram (ECG) electrodes is presented, along with their relationship to performance properties including electrical, material, ECG signal quality, fabric hand (sensory perception and quality), and physiological comfort. Considerations and insights into the textile fiber and yarn morphology, electrode structure, design, and construction are outlined. In addition, relevant and upcoming standards for e-textile testing and performance evaluation are summarized. This work serves to organize requirements for ECG textile electrodes into a general reference framework from a bottom-up approach, which can better guide the material selection and design of ECG textile electrodes for wearable applications.