Extensive defects and functional impairments in oral and maxillofacial tissues pose significant clinical challenges, with current standard treatments facing inherent limitations. Tissue engineering, integrating seed cells, scaffolds, and bioactive factors, offers a promising regenerative approach. Human umbilical cord mesenchymal stem cells (hUCMSCs) have emerged as a promising and clinically advantageous cell source due to their robust multi-lineage potency, immunomodulatory capacity, low immunogenicity, and non-invasive procurement. However, their therapeutic efficacy relies on delivery systems that ensure cell retention and fate control. This review provides a comprehensive analysis of hUCMSC-based strategies (including both cellular and exosome-mediated approaches) combined with biological scaffolds for tissue engineering. It details the biological characteristics of hUCMSCs, reviews the design, performance, and functionalization strategies (e.g., surface modification, peptide conjugation, and ionic doping) of key scaffold materials (bioceramics, biologically derived scaffolds, polymers, and composites), and highlights their applications in regenerating oral and maxillofacial bone, cartilage, periodontal, and pulp-dentin tissues. The discussion concludes with an examination of current translational challenges and future perspectives, aiming to serve as a reference for advancing next-generation regenerative therapies.