  The observation of lepton flavour violation (LFV) in interactions involving
charged leptons would be an unambiguous sign of physics beyond the Standard
Model of particle physics. Given that muons can be produced at high
intensities, searches for LFV with muons are particularly sensitive.
  In a global initiative, ongoing and upcoming experiments are aiming to
discover physics beyond the Standard Model in the three golden muon LFV
channels: $\mu\to e\gamma$, $\mu\to eee$ and $\mu$-to-$e$ conversion on nuclei.
With innovative detector concepts and new muon beam lines, these experiments
will be able to investigate muon LFV in the coming years with sensitivities
improved by up to four orders of magnitude compared to past searches.
  The current status of muon LFV searches is discussed and the ongoing MEG II
and DeeMe experiments as well as the upcoming Mu2e, COMET and Mu3e experiments
are presented.
