Detection and quantification of a variety of micro- and nanoscale entities, e.g. molecules, cells, and particles, are crucial components of modern biomedical research, in which biosensing platform technologies play a vital role. Confronted with the drastic global demographic changes, future biomedical research entails continuous development of new-generation biosensing platforms targeting even lower costs, more compactness, and higher throughput, sensitivity and selectivity. Among a wide choice of fundamental biosensing principles, magnetic sensing technologies enabled by magnetic field sensors and magnetic particles offer attractive advantages. The key features of a magnetic sensing format include the use of commercially available magnetic field sensing elements, e.g. magnetoresistive sensors which bear huge potential for compact integration, a magnetic field sensing mechanism which is free from interference by complex biomedical samples, and an additional degree of freedom for the on-chip handling of biochemical species rendered by magnetic labels. In this review, we highlight the historical basis, routes, recent advances and applications of magnetic biosensing platform technologies based on magnetoresistive sensors.