Future wearable electronics and smart textiles face a major challenge in the development of energy storage devices that are high-performing while still being flexible, lightweight, and safe. Fiber supercapacitors are one of the most promising energy storage technologies for such applications due to their excellent electrochemical characteristics and mechanical flexibility. Over the past decade, researchers have put in tremendous effort and made significant progress on fiber supercapacitors. It is now the time to assess the outcomes to ensure that this kind of energy storage device will be practical for future wearable electronics and smart textiles. While the materials, fabrication methods, and energy storage performance of fiber supercapacitors have been summarized and evaluated in many previous publications, this review paper focuses on two practical questions: Are the reported devices providing sufficient energy and power densities to wearable electronics? Are the reported devices flexible and durable enough to be integrated into smart textiles? To answer the first question, we not only review the electrochemical performance of the reported fiber supercapacitors but also compare them to the power needs of a variety of commercial electronics. To answer the second question, we review the general approaches to assess the flexibility of wearable textiles and suggest standard methods to evaluate the mechanical flexibility and stability of fiber supercapacitors for future studies. Lastly, this article summarizes the challenges for the practical application of fiber supercapacitors and proposes possible solutions.