Electrospinning is attracting close interest as a versatile fabrication method for one dimensional mesostructured organic, inorganic and hybrid nanomaterials of controlled dimensions prepared as random or oriented continuous nanofibres with possibilities of ordered internal morphologies such as core-sheath, hollow or porous fibre, or even multichannelled microtube arrangements. The dimensionality, directionality and compositional flexibility of electrospun nanofibres and mats are increasingly being investigated for the targeted development of electrode and electrolyte materials, where the specific properties associated with nanoscale features such as high surface area and aspect ratios, low density and high pore volume allow performance improvements in energy conversion and storage devices. We present here a review on the application of electrospinning for the design and fabrication of architectured, nanofibrous materials for dye sensitised solar cells, fuel cells, lithium ion batteries and supercapacitors, with particular emphasis on improved energy and power density imparted by performance improvement to, inter alia, ionic conductivity, cyclability, reversibility, interfacial resistance and electrochemical stability, as well as mechanical strength, of electrospun electrode and electrolyte components.