Globally, the demand for improved health care delivery while managing escalating costs is a major challenge. Measuring the biomagnetic fields that emanate from the human brain already impacts the treatment of epilepsy, brain tumours and other brain disorders. This roadmap explores how superconducting technologies are poised to impact health care. Biomagnetism is the study of magnetic fields of biological origin. Biomagnetic fields are typically very weak, often in the femtotesla range, making their measurement challenging. The earliest in vivo human measurements were made with room-temperature coils. In 1963, Baule and McFee (1963 Am. Heart J. 55 95-6) reported the magnetic field produced by electric currents in the heart ('magnetocardiography'), and in 1968, Cohen (1968 Science 161 784-6) described the magnetic field generated by alpha-rhythm currents in the brain ('magnetoencephalography'). Subsequently, in 1970, Cohen et al (1970 Appl. Phys. Lett. 16 278-80) reported the recording of a magnetocardiogram using a Superconducting QUantum Interference Device (SQUID). Just two years later, in 1972, Cohen (1972 Science 175 664-6) described the use of a SQUID in magnetoencephalography. These last two papers set the scene for applications of SQUIDs in biomagnetism, the subject of this roadmap. The SQUID is a combination of two fundamental properties of superconductors. The first is flux quantization - the fact that the magnetic flux Φ in a closed superconducting loop is quantized in units of the magnetic flux quantum, Φ0 ≡ h/2e, ≈ 2.07 × 10-15 Tm2 (Deaver and Fairbank 1961 Phys. Rev. Lett. 7 43-6, Doll R and Nabauer M 1961 Phys. Rev. Lett. 7 51-2). Here, h is the Planck constant and e the elementary charge. The second property is the Josephson effect, predicted in 1962 by Josephson (1962 Phys. Lett. 1 251-3) and observed by Anderson and Rowell (1963 Phys. Rev. Lett. 10 230-2) in 1963. The Josephson junction consists of two weakly coupled superconductors separated by a tunnel barrier or other weak link. A tiny electric current is able to flow between the superconductors as a supercurrent, without developing a voltage across them. At currents above the 'critical current' (maximum supercurrent), however, a voltage is developed. In 1964, Jaklevic et al (1964 Phys. Rev. Lett. 12 159-60) observed quantum interference between two Josephson junctions connected in series on a superconducting loop, giving birth to the dc SQUID. The essential property of the SQUID is that a steady increase in the magnetic flux threading the loop causes the critical current to oscillate with a period of one flux quantum. In today's SQUIDs, using conventional semiconductor readout electronics, one can typically detect a change in Φ corresponding to 10-6 Φ0 in one second. Although early practical SQUIDs were usually made from bulk superconductors, for example, niobium or Pb-Sn solder blobs, today's devices are invariably made from thin superconducting films patterned with photolithography or even electron lithography. An extensive description of SQUIDs and their applications can be found in the SQUID Handbooks (Clarke and Braginski 2004 Fundamentals and Technology of SQUIDs and SQUID Systems vol I (Weinheim, Germany: Wiley-VCH), Clarke and Braginski 2006 Applications of SQUIDs and SQUID Systems vol II (Weinheim, Germany: Wiley-VCH)). The roadmap begins (chapter 1) with a brief review of the state-of-the-art of SQUID-based magnetometers and gradiometers for biomagnetic measurements. The magnetic field noise referred to the pick-up loop is typically a few fT Hz-1/2, often limited by noise in the metallized thermal insulation of the dewar rather than by intrinsic SQUID noise. The authors describe a pathway to achieve an intrinsic magnetic field noise as low as 0.1 fT Hz-1/2, approximately the Nyquist noise of the human body. They also descibe a technology to defeat dewar noise. Chapter 2 reviews the neuroscientific and clinical use of magnetoencephalography (MEG), by far the most widespread application of biomagnetism with systems containing typically 300 sensors cooled to liquid-helium temperature, 4.2 K. Two important clinical applications are presurgical mapping of focal epilepsy and of eloquent cortex in brain-tumor patients. Reducing the sensor-to-brain separation and the system noise level would both improve spatial resolution. The very recent commercial innovation that replaces the need for frequent manual transfer of liquid helium with an automated system that collects and liquefies the gas and transfers the liquid to the dewar will make MEG systems more accessible. A highly promising means of placing the sensors substantially closer to the scalp for MEG is to use high-transition-temperature (high-T c) SQUID sensors and flux transformers (chapter 3). Operation of these devices at liquid-nitrogen temperature, 77 K, enables one to minimize or even omit metallic thermal insulation between the sensors and the dewar. Noise levels of a few fT Hz-1/2 have already been achieved, and lower values are likely. The dewars can be made relatively flexible, and thus able to be placed close to the skull irrespective of the size of the head, potentially providing higher spatial resolution than liquid-helium based systems. The successful realization of a commercial high-T c MEG system would have a major commercial impact. Chapter 4 introduces the concept of SQUID-based ultra-low-field magnetic resonance imaging (ULF MRI) operating at typically several kHz, some four orders of magnitude lower than conventional, clinical MRI machines. Potential advantages of ULF MRI include higher image contrast than for conventional MRI, enabling methodologies not currently available. Examples include screening for cancer without a contrast agent, imaging traumatic brain injury (TBI) and degenerative diseases such as Alzheimer's, and determining the elapsed time since a stroke. The major current problem with ULF MRI is that its signal-to-noise ratio (SNR) is low compared with high-field MRI. Realistic solutions to this problem are proposed, including implementing sensors with a noise level of 0.1 fT Hz-1/2. A logical and exciting prospect (chapter 5) is to combine MEG and ULF MRI into a single system in which both signal sources are detected with the same array of SQUIDs. A prototype system is described. The combination of MEG and ULF MRI allows one to obtain structural images of the head concurrently with the recording of brain activity. Since all MEG images require an MRI to determine source locations underlying the MEG signal, the combined modality would give a precise registration of the two images; the combination of MEG with high-field MRI can produce registration errors as large as 5 mm. The use of multiple sensors for ULF MRI increases both the SNR and the field of view. Chapter 6 describes another potentially far-reaching application of ULF MRI, namely neuronal current imaging (NCI) of the brain. Currently available neuronal imaging techniques include MEG, which is fast but has relatively poor spatial resolution, perhaps 10 mm, and functional MRI (fMRI) which has a millimeter resolution but is slow, on the order of seconds, and furthermore does not directly measure neuronal signals. NCI combines the ability of direct measurement of MEG with the spatial precision of MRI. In essence, the magnetic fields generated by neural currents shift the frequency of the magnetic resonance signal at a location that is imaged by the three-dimensional magnetic field gradients that form the basis of MRI. The currently achieved sensitivity of NCI is not quite sufficient to realize its goal, but it is close. The realization of NCI would represent a revolution in functional brain imaging. Improved techniques for immunoassay are always being sought, and chapter 7 introduces an entirely new topic, magnetic nanoparticles for immunoassay. These particles are bio-funtionalized, for example with a specific antibody which binds to its corresponding antigen, if it is present. Any resulting changes in the properties of the nanoparticles are detected with a SQUID. For liquid-phase detection, there are three basic methods: AC susceptibility, magnetic relaxation and remanence measurement. These methods, which have been successfully implemented for both in vivo and ex vivo applications, are highly sensitive and, although further development is required, it appears highly likely that at least some of them will be commercialized.