The possible existence of the muon to electron and gamma decay predicted by many new physics scenarios is investigated by stopping positive muons in a very thin target and measuring emitted photons and positrons with the best possible resolutions. Photons are measured by a 2.7 ton ultra pure liquid xenon detector while positron trajectories are measured in a specially designed gradient magnetic field by low-mass drift chambers and precisely timed by scintillation counters. A first phase of the experiment (MEG) ended in 2016, and excluded the existence of the decay with branching ratios larger than 4.2x10**(-13) (90% C.L.). This provides approximately 30 times stronger constraints on a variety of new physics models than previous experiments. In the second phase (MEG II), most of the detectors have been upgraded by adopting up-to-date technologies to improve the search sensitivity by another order of magnitude down to O(10**(-19) ). MEG II will pursue new physics beyond the Standard Model complementary to high energy collider experiments with a compatible or even higher sensitivity.
