The absolute mass scale of neutrinos is an intriguing open question in contemporary physics. The as-yet-unknown mass of the lightest and, at the same time, most abundant massive elementary particle species bears fundamental relevance to theoretical particle physics, astrophysics, and cosmology. The most model-independent experimental approach consists of precision measurements of the kinematics of weak decays, notably tritium β decay. With the KATRIN experiment, this direct neutrino-mass measurement has entered the sub-eV domain, recently pushing the upper limit on the electron-based neutrino mass down to 0.8 eV (90% CL) on the basis of first-year data out of ongoing, multiyear operations. Here, we review the experimental apparatus of KATRIN, the progress of data taking, and initial results. While KATRIN is heading toward the target sensitivity of 0.2 eV, other scientific goals are pursued. We discuss the search for light sterile neutrinos and an outlook on future keV-scale sterile-neutrino searches as well as further physics opportunities beyond the Standard Model
