3D bioprinting has transformed skin tissue regeneration by enabling fabrication of skin-like structures with precisely controlled properties. This review critically examines recent advances and challenges in 3D bioprinting for skin tissue engineering (2020–2026), organized around a unifying materials-design framework linking bioink properties to wound healing phase requirements and printing technology selection. Wound healing mechanisms, cell types, bioink formulations, and major bioprinting technologies (inkjet, extrusion, laser-assisted, light-curing) are comparatively evaluated for resolution, cell viability, material compatibility, and scalability. 3D bioprinting enables vascular network formation, nerve regeneration, and regrowth of skin appendages including sweat glands, hair follicles, and pigmentation, while patient-specific constructs reduce rejection risk and improve outcomes. Four clinical niches where bioprinting offers genuine advantage are identified: chronic wounds, cosmetically critical areas, full-thickness burns exceeding 40% total body surface area, and in vitro pharmaceutical testing. Existing approaches remain limited in mimicking physiological complexity, multi-material harmony, and long-term stability. Critical gaps persist in elastin regeneration, matrix mechanotransduction, immune-material interactions, and transition to GMP-compliant manufacturing. Regulatory pathways, scalability, and cost-effectiveness as underaddressed translational barriers are explicitly evaluated. Further progress requires convergence of stem cell technology, advanced bioink design, and AI-driven optimization. Interdisciplinary collaboration remains essential to advance bioprinting toward clinical application in severe skin injuries and regenerative medicine.