In cell-free scaffold tissue engineering (TE), an essential prerequisite is the scaffold design to promote cellular activities and tissue formation. The success is greatly dependent upon the nature of the scaffold including the composition, topography, and mechanical performance. Recent TE approaches use textile technologies to create biomimetic and functional scaffolds similar to the extracellular matrix (ECM). The hierarchical architecture of fiber to yarn to fabric allows precise size-to-scale design. Moreover, textile technologies offer a high degree of manufacturing precision, reproducibility, and potential industrial scalability. Although research in industry and academia has increased significantly over the past years, current fibrous scaffold designs don't fully exploit the potential and diversity of yarn and fabric structures. This review emphasizes hollow tubular textile-based scaffolds that aim to replace vasculature and respiratory tissues. The different techniques, that is, electrospinning, weaving, knitting, and braiding are discussed and the effect of the fiber, yarn, and fabric assembly is highlighted. The design of multi-layer hybrid structures, combining conventional textile techniques and electrospinning can address current challenges. Prospects of structural design in TE scaffold fabrication can anticipate profiled fibers, and complex pattern designs to fully exploit the potential of textile technologies for tissue-engineered scaffolds.