Precision measurements are becoming powerful searchlight for new physics beyond the Standard Model, probing energy scale and parameter spaces outside the reach of existing collider in many scenarios, and promise to deliver more in the near future. In this talk I will discuss two precision observables in the lepton setor: the electron electric dipole moment and lepton flavor-violating processes. I will demonstrate the power of these precision measurements through both general dimensional analysis and discussion of specific scenarios, such as SUSY and QULE operators. I will then discuss how a high energy muon collider can not only put competitive bounds on some of these precision observables, but also directly probe the new physics given an indirect discovery from the precision sector.