Biomedical nanomagnetics is a multidisciplinary area of research in science, engineering and medicine with broad applications in imaging, diagnostics and therapy. Recent developments offer exciting possibilities in personalized medicine provided a truly integrated approach, combining chemistry, materials science, physics, engineering, biology and medicine, is implemented. Emphasizing this perspective, here we address important issues for the rapid development of the field, i.e., magnetic behavior at the nanoscale with emphasis on the relaxation dynamics, synthesis and surface functionalization of nanoparticles and core-shell structures, biocompatibility and toxicity studies, biological constraints and opportunities, and in vivo and in vitro applications. Specifically, we discuss targeted drug delivery and triggered release, novel contrast agents for magnetic resonance imaging, cancer therapy using magnetic fluid hyperthermia, in vitro diagnostics and the emerging magnetic particle imaging technique, that is quantitative and sensitive enough to compete with established imaging methods. In addition, the physics of self-assembly, which is fundamental to both biology and the future development of nanoscience, is illustrated with magnetic nanoparticles. It is shown that various competing energies associated with self-assembly converge on the nanometer length scale and different assemblies can be tailored by varying particle size and size distribution. Throughout this paper, while we discuss our recent research in the broad context of the multidisciplinary literature, we hope to bridge the gap between related work in physics/chemistry/engineering and biology/medicine and, at the same time, present the essential concepts in the individual disciplines. This approach is essential as biomedical nanomagnetics moves into the next phase of innovative translational research with emphasis on development of quantitative in vivo imaging, targeted and triggered drug release, and image guided therapy including validation of delivery and therapy response.