Novel core fibers have a wide range of applications in optics, as sources, detectors and nonlinear response media. Optoelectronic, and even electronic device applications are now possible, due to the introduction of methods for drawing fibres with a semiconductor core. This review examines progress in the development of glass-clad, crystalline core fibres, with an emphasis on semiconducting cores. The underlying materials science and the importance of post-processing techniques for recrystallization and purification are examined, with achievements and future prospects tied to the phase diagrams of the core materials.