The field of bioprinting has witnessed remarkable advancements in recent years, revolutionizing the fabrication of biological tissues and organs for research, pharmaceutical testing, and potential clinical applications. This progress is attributed to the development of diverse bioprinting technologies, ranging from low-cost models utilizing microextrusion-based technology to high-end systems employing droplet-based and laser-assisted techniques. These technologies offer varying levels of precision, build volume, and material compatibility, catering to a wide spectrum of research needs. Notably, microfluidic-based bioprinting has emerged as a transformative approach, enabling fast, continuous switching and mixing of materials, achieving nearly single-cell printing resolution. Moreover, support-free multiaxial printing and high-resolution printing using focused light have shown promise in enhancing geometric complexity and cell viability. The integration of modular print heads and the potential for in situ bioprinting are poised to further expand the capabilities of bioprinting technologies. Despite these advancements, current bioprinting systems exhibit certain limitations, including constraints in motion axes, printing volume, and material compatibility. Addressing these challenges will be crucial in realizing the full potential of bioprinting for tissue engineering and regenerative medicine applications. This review provides valuable insights into the diverse range of bioprinting methods, systems and their collective potential to advance tissue engineering and regenerative medicine.