Precision measurements of electron capture decays are sensitive methods to probe physics beyond the standard model (BSM) in the neutrino sector since momentum conservation between the emitted neutrino and the recoiling daughter nucleus is sensitive to any new physics that couples to the neutrino mass. The “Beryllium-7 Electron capture in Superconducting Tunnel junctions” (BeEST) experiment precisely measures the eV-scale radiation that follows the radioactive decay of Be-7 nuclei that are implanted into sensitive superconducting tunnel junction (STJ) quantum sensors. Sterile neutrinos in the keV mass range would reduce the recoil energy of the Li-7 daughter and produce additional peaks at lower energy in the spectrum as a signature. STJs are ideally suited for measurements of this type due to their high resolution at the low recoil energies in EC decay and their high count rate capabilities. The initial phase of the BeEST with a single STJ sensor already provides the most stringent limits on sterile neutrinos in the mass range from 100 to 800 keV. We present an introduction to STJ quantum sensors and describe the various phases of the BeEST experiment.