Nanofibres, core-shell nanofibres, as well as hollow nanofibres and nanotubes based on polymers, serve as a platform for a broad range of applications as filters, textiles, in photonics, sensors, catalysis, or in medicine and pharmacy. Such nanoobjects become available by techniques such as the well-known electrospinning and the more recently developed co-electrospinning of nanofibres. Electrospinning takes place in the latter case by two or more concentrically arranged dies that yield core-shell fibres or fibres with droplet-like inclusions arranged along the centre of the fibres, where the inclusions are composed of polymers, low-molar-mass synthetic functional units, or molecules of biological origins such as proteins. Furthermore, template methods have been developed using electrospun nanofibres or a porous substrate, which yield core-shell fibres of complex architectures, with or without gradient structures or hollow nanofibres and nanotubes. These techniques are not restricted to polymers of synthetic and natural origin, but are able-based on precursor substances-to deliver nanofibres and nanotubes also composed of metals, glasses, and ceramics. Furthermore, these preparation techniques allow the direct introduction into these nanostructures of specific functional compounds such as semiconductor or catalytic nanoparticles and chromophores, in addition to enzymes, proteins, microorganisms, etc. during the preparation process in a very gentle way. Of particular interest are such nanostructures in medicine and pharmacy, for instance, as scaffolds for tissue engineering or as drug-delivery systems for tumour therapy.