Brain functions are associated with electric currents flowing in the brain tissue. The spatiotemporal distribution of neural current thus provides us with valuable information regarding questions such as where and when specific functions of interest take place in the brain, and how different functional areas are connected to each other. Such information can be used in studying normal brain development and mechanisms of neurological disorders. The most precise way of reconstructing the neural currents in a non-invasive fashion is by measuring the brain’s magnetic field with very sensitive sensors. This technique is called magnetoencephalography (MEG). I will review the basic principles and applications of MEG and discuss some of our past, present, and future research on instrumentation, mathematical modeling, signal processing, and analysis in MEG. The focus will be on how physics models based on first principles can help reach unprecedented precision in the reconstruction of neural activity, which in turn has a significant impact on neuroscience and neurology findings that can help people at individual and societal levels. An example of recent progress in MEG is the introduction of novel optically pumped magnetometer (OPM) sensors that can be attached directly on the head in flexible formations. I will highlight our recent work, which suggests optimal geometrical arrangements of OPM sensors to robustly capture very high spatial frequencies of the magnetic field, potentially leading to sub-millimeter resolution in MEG-based imaging of brain functions.