This article reviews recent progress in the development of biosupercapacitors - supercapacitors fabricated using biological materials. In conventional biosupercapacitors the biomaterial serves as the pseudocapacitive component, while in self-charging biodevices the biocomponent also functions as the biocatalyst. The performance characteristics of biosupercapacitors are summarized and characterized in the perspective of the broader family of electric power devices, including biodevices. Self-charging biosupercapacitors show great promise in pulse-power delivery at the milliwatt level, typically greatly exceeding the capability of free-running bio-fuel and bio-solar cells. Thus, chemical biosupercapacitors might be suitable for powering a new generation of miniaturized electronic applications, including those intended for use in medical technology, while solar biodevices might be used as highly functional, but at the same time low-cost, environmentally friendly, and technically undemanding electric power sources.