Supercapacitors (SCs) are energy storage devices which have high power density and long cycle life. Conventional SCs have two-dimensional planar structures. As a new family of SCs, fiber SCs utilize one-dimensional cylindrically shaped fibers as electrodes. They have attracted significant interest since 2011 and have shown great application potential either as micro-scale devices to complement or even replace micro-batteries in miniaturized electronics and microelectromechanical systems or as macro-scale devices for wearable electronics or smart textiles. This tutorial review provides an essential introduction to this new field. We first introduce the basics of performance evaluation for fiber SCs as a foundation to understand different research approaches and the diverse performance metrics reported in the literature. Next, we summarize the current state-of-the-art progress in structure design and electrode fabrication of fiber SCs. This is followed by a discussion on the integration of multiple fiber SCs and the combination with other energy harvesting or storage devices. Last, we present our perspectives on the future development of fiber SCs and highlight key technical challenges with the hope of stimulating further research progress.