The presented article discusses recent advances in biomedical applications of classical Magnetohydrodynamics (MHD), with a focus on operating principles and associated material considerations. These applications address novel approaches to common biomedical problems from micro-particle sorting for lab-on-a-chip devices to advanced physiological monitoring techniques. 100 papers in the field of MHDs were reviewed with a focus on studies with direct biomedical applications. The body of literature was categorized into three primary areas of research including Material Considerations for MHD Applications, MHD Actuation Devices, and MHD Sensing Techniques. The state of the art in the field was examined and research topics were connected to provide a wide view of the field of biomedical MHDs. As this field develops, the need for advanced simulation and material design will continue to increase in importance in order to further expand its reach to maturity. As the field of biomedical MHDs continues to grow, advances towards micro-scale transitions will continue to be made, maintaining its clinically driven nature and moving towards real-world applications.