Lepton Flavour violation in muon decays

The search for lepton flavour violation in charged lepton decays is highly sensitive to physics beyond the Standard Model. Among the possible processes, $\mu$-decays are considered to have the largest discovery potential in most of the standard model extensions. Many searches has been performed in the past, however no evidence has been found so far. Four dedicated experiments are in advanced state of preparation to improve the current associated sensibilities by 1-4 order of magnitudes for the charged lepton flavour violating processes $\mu\rightarrow \rm{e}\gamma$, $\mu\rightarrow \rm{e}$ conversion and $\mu\rightarrow \rm{eee}$. In this paper I present physics motivations, experimental challenges and construction status of the experiments, which are the studying above mentioned processes.