The unending demand for portable, flexible, and even wearable electronic devices that have an aesthetic appeal and unique functionality stimulates the development of advanced power sources that have excellent electrochemical performance and, more importantly, shape versatility. The challenges in the fabrication of next-generation flexible power sources mainly arise from their limited form factors, which prevent their facile integration into differently shaped electronic devices, and from the lack of reliable electrochemical materials that exhibit optimized attributes and suitable processability. This review describes the technological innovations and challenges associated with flexible energy storage and conversion systems such as lithium-ion batteries and supercapacitors, along with an overview of the progress in flexible proton exchange membrane fuel cells (PEMFCs) and solar cells. In particular, recently highlighted cable-type flexible batteries with extreme omni-directional flexibility are comprehensively discussed.