Biomagnetism involves the measurement and analysis of very weak local magnetic fields of living organisms and various organs in humans. Such fields can be of physiological origin or due to magnetic impurities or markers. This paper reviews existing and prospective applications of biomagnetism in clinical research and medical diagnostics. Currently, such applications require sensitive magnetic SQUID sensors and amplifiers. The practicality of biomagnetic methods depends especially on techniques for suppressing the dominant environmental electromagnetic noise, and on suitable nearly real-time data processing and interpretation methods. Of the many biomagnetic methods and applications, only the functional studies of the human brain (magnetoencephalography) and liver susceptometry are in clinical use, while functional diagnostics of the human heart (magnetocardiography) approaches the threshold of clinical acceptance. Particularly promising for the future is the ongoing research into low-field magnetic resonance anatomical imaging using SQUIDs.