Status and perspectives of Lepton Flavour Violation experiments with muons

Lepton Flavour Violation effects are predicted in several extensions of the Standard Model at a measurable level. Since the Standard Model background, even including ν oscillations and mixing, is completely negligible, the observation of such effects would be a strong evidence for New Physics beyond the Standard Model, while a non observation with high precision experiments would put severe constraints on possible Standard Model extensions. In this talk I review the present status and the future perspectives of the Lepton Flavour Violation experiments involving 's and discuss the sensitivity improvements which could be obtained from new high intensity machines coupled with high resolution detectors.