Increasing efforts have been made in tissue engineering (TE) research for novel biomaterials and scaffolds that can efficiently support bone tissue regeneration and repair. Textile-based technologies are predefined manufacturing processes of particular interest since they allow for producing finely tuned fiber-based structures with controlled three-dimensional architecture and improved mechanical properties. Highly reproducible scaffolds can be achieved with interconnected macro- and micro-porosity suitable for controlling cell functions and guiding bone tissue regeneration and repair. Herein, the recent studies dealing with the processing methodologies, physical properties, and biocompatibility of fiber-based scaffolds for bone TE applications are overviewed. The fundamentals and application of silk fibroin (SF) protein as biomaterial for scaffolds production, made up of micro- and nano-fibers are also considered. The promising outcomes of such investigations are summarized and discussed in depth.