Electrospinning is a promising approach for the development of fibrous tissue engineering (TE) scaffolds suitable for hard and soft tissues. Apart from physicomechanical properties, electrospun fibers are required to incorporate bioactive cues to control cellular functions, including facilitating biomineralization and osteogenic differentiation in case of bone TE, as well as vascularization, to support successful tissue regeneration. In recent years, bioactive glass (BG) addition to electrospun biopolymer fibers has shown promising results in enhancing the properties of fibers, including the improvement of biological performance. In this article, a comprehensive overview of BG‐containing electrospun polymer composite fibers is presented, identifying the parameters that affect the mechanical properties as well as the biological response in vivo and in vitro. Subsequently, the effects of BG addition on the properties of the scaffolds are discussed. Recent developments in the fields of bone regeneration, wound healing, and drug delivery using BG‐containing electrospun fibrous scaffolds are described in detail. Essential aspects related to BG‐polymer composite fibers for translational research in TE are highlighted for future research in this field.