Abstract.In the next decade Charged Lepton Flavour Violation (CLFV) experiments will play a key role in the search for new physics. Given that flavour oscillations occur among neutrinos, unmeasurably small amplitudes are expected for CLFV processes, while in many new physics scenarios such processes are strongly enhanced. A new generation of experiments looking for CLFV muon decays will be performed at the Paul Scherrer Institut (MEG II, Mu3e), at Fermilab (Mu2e) and at J-Parc (DeeMee, COMET), with sensitivities improved by one or two order of magnitudes with respect to current limits. The MEG experiment has performed the most recent improvement in the search for the CLFV decay μ + → e + γ. With the analysis of half of the collected statistics, a new upper limit on the branching ratio has been set BR(μ → eγ) < 5.7 × 10 −13 at 90% CL, and the final result is soon to be released. A substantial improvement of MEG results requires an improvement of detector performances, in order to reject the background contributions which limit the signal sensitivity. This will be carried out by a short-term upgrade of the apparatus, MEG II. The major modifications of the experimental apparatus consist in the replacement of the current positron tracking system with a new high transparency and high granularity spectrometer and the substitution and rearrangement of some of the photosensors in the liquid-xenon photon detector. MEG II will start taking data in 2016, with a sensitivity on the μ + → e + γ decay of about 5 × 10 −14 . Therefore as MEG performed the last improvement in the search for CLFV, MEG II will start a new era probing unexplored regions of new physics scenarios.