Bioprinting has emerged as a transformative technology in biofabrication, enabling the precise spatial arrangement of biomaterials, living cells, and bioactive factors to generate functional three-dimensional biological constructs. Recent advances are redefining the scope and impact of this field through innovations in both materials and methodologies. Multimaterial and multiscale printing strategies are enhancing the ability to replicate the hierarchical architecture and functional gradients of native tissues, while the valorization of waste-derived biomaterials for bioink formulation is introducing sustainable solutions without compromising performance. The integration of bioprinting with organ-on-a-chip systems is providing highly sophisticated in vitro models for disease research and drug discovery, and in situ bioprinting techniques are opening new possibilities for direct, patient-specific tissue repair. Parallel to these developments, 4D bioprinting introduces the dimension of time, allowing printed constructs to change shape, properties, or function in response to environmental stimuli. The application of artificial intelligence in process monitoring and quality control is improving reproducibility, predictive accuracy, and manufacturing efficiency, thus paving the way for standardized production. Looking ahead, the emerging concept of 5D bioprinting—integrating spatial, temporal, and functional control—suggests a paradigm shift in the design and manufacturing of living systems. Collectively, these advances are broadening the technological capabilities of biofabrication and accelerating the translation of bioprinting from experimental settings toward transformative clinical and industrial applications. This review synthesizes current progress while outlining the opportunities and challenges that will shape the next generation of bioprinting technologies.