Precision spectroscopy of hydrogen-like atoms is a powerful method to study fundamental interactions and constants. In particular, exotic atoms involving muons are useful for a precision test of bound-state QED theory and a search for physics beyond the Standard Model. Several precision spectroscopy projects of muonic systems are in progress at J-PARC, where the highest-intensity pulsed muon beam is provided. The MuSEUM collaboration aims to measure the ground-state hyperfine splitting (HFS) of muonium and determine the muon-to-electron mass ratio. The first phase of the experiment has been started and the microwave resonance of the muonium HFS was successfully observed. Toward solving an unsolved problem in the proton charge radius, laser spectroscopy of muonic hydrogen was newly proposed to measure the ground-state HFS and determine the proton Zemach radius. This experiment is in preparation and a feasibility study was performed.