Not yet reviewed by Pith; the record is open.

At the J-PARC Muon Science Facility (MUSE), the MuSEUM collaboration is now performing new precision measurements of the ground state hyperfine structure (HFS) of both muonium and muonic helium atoms. High-precision measurements of the muonium ground-state HFS are recognized as one of the most sensitive tools for testing bound-state quantum electrodynamics theory to precisely probe the standard model and determine fundamental constants of the positive muon magnetic moment and mass. The same technique can also be employed to measure muonic helium HFS, obtain the negative muon magnetic moment and mass, and test and improve the theory of the three-body atomic system. Measurements at zero magnetic field have already yielded more accurate results than previous experiments for both muonium and muonic helium atoms. High-field measurements are now ready to start collecting data using the world's most intense pulsed muon beam at the MUSE H-line. We aim to improve the precision of previous measurements ten times for muonium and a hundred times or more for muonic helium. We review all the key developments for these new measurements, focusing on the high-field experiment, and report the latest results and prospects.