Lepton flavour conservation, being an accidental symmetry in the Standard Model (SM) of particle physics, is prone to be violated in most of the models of new physics. Although lepton flavour violation (LFV) has been already observed in the form of neutrino oscillations, the consequent effect in the charged lepton sector is unobservably small. Hence, charged LFV is both a very sensitive probe for physics beyond the SM and a phenomenon whose observation would provide an unambiguous evidence for such new physics. The goal of the MEG II experiment is the search for the LFV decay $\mu \to e \gamma$, with a sensitivity below $10^{-13}$, a factor 10 better than the phase-1 MEG experiment. The construction and commissioning of MEG II have been recently completed and the first physics data are expected to be collected at the end of year 2021. In this contribution I will present the current status of the experiment and its expected performances. A recent result for the search of the $\mu \to e X$ with $X \to \gamma \gamma$ $\mu \to e X$ with $X \to \gamma \gamma$ decay in the dataset of MEG will be also reviewed.