This review article aims to provide an overview of superconducting magnetic quantum sensors and their applications in the biomedical field, particularly in the neurological field. These quantum sensors are based on superconducting quantum interference devices (SQUIDs), the operating principles of which will be presented along with the most relevant characteristics. Emphasis will be placed on the magnetic flux and magnetic field noise, which are essential for applications, especially brain investigations requiring ultra-high magnetic field sensitivity. The main configurations of SQUID magnetometers used for highly sensitive applications will be shown, stressing their design aspects. In particular, the configurations based on the superconducting flux transformer and the multiloop will be explained. We will discuss the most critical application of SQUID magnetometers, magnetoencephalography, which measures the weak magnetic signals produced by neuronal currents. Starting from the realization of a multichannel system for magnetoencephalography, we will present an accurate comparison with recent systems using optically pumped magnetometers. Finally, we will discuss the main clinical applications of magnetoencephalography.