Carbon nanotubes (CNTs), as one-dimensional carbon nanomaterials, exhibit exceptional electrical conductivity, mechanical strength, and chemical stability, making them highly suitable for applications in energy storage and wearable devices. Despite Floating catalyst chemical vapor deposition (FCCVD) is a scalable, one-step method capable of fabricating CNT aerogels, fibers, and sheets. A key advantage of FCCVD lies in its tunability of CNT properties such as aspect ratio, crystallinity, wall number, and chirality during synthesis, which are critical parameters for optimizing electrochemical performance. However, as-synthesized CNTs typically contain impurities such as residual catalysts, graphitic impurities and amorphous carbon, necessitating post-synthesis purification and functionalization to improve their compatibility with polymer matrices and composite systems. CNTs are widely used as active materials and conductive networks in batteries and supercapacitors, contributing to enhanced both energy and power density. Despite these advantages, CNT based devices still face challenges including variability in properties, cost, scalability, and integration issues such as structural non-uniformity, and inconsistent assemblies that limit cycle life and reproducibility. Various purification and functionalization strategies have been developed to improve the CNT quality for device integration. This review outlines FCCVD-based CNT synthesis, purification and functionalization methods, and highlights the critical roles CNTs play in advancing next-generation lithium-ion batteries and supercapacitors.