The development of flexible and stretchable wearable electronics has significantly advanced smart fabrics, biomedical devices, and healthcare technologies. However, these devices often face challenges from mechanical deformations that disrupt signals, emphasizing the need for strain‐insensitive architectures to maintain functionality under varying strain conditions. Progress in this field relies on multifunctional, strain‐insensitive microfibers and nanofibers (NFs) to ensure consistent performance while minimizing signal interference caused by mechanical stress. This review highlights the advantages of fibers for flexible, stretchable, and strain‐insensitive wearable electronics, analyzing materials, fabrication methods, and design strategies that optimize strain insensitivity in single free‐standing microfibers (SFMs) and NF‐based devices. It emphasizes maintaining mechanical and electrical stability under large strains through strategic material selection, advanced fiber spinning techniques, and innovative structural designs. While emphasizing SFMs, this review also provides a concise exploration of the role of NFs within this context. The applications of SFMs in wearable electronics, particularly as conductors, sensors, and components in smart textiles, are discussed with an emphasis on strain insensitivity. The review concludes by addressing challenges in this evolving field of wearable electronics and outlining future research directions, offering insights to drive innovations in fiber‐based wearable electronics for reliable, lightweight, breathable, user‐friendly, and high‐performance wearable devices.