  The muon is playing a unique role in sub-atomic physics. Studies of muon
decay both determine the overall strength and establish the chiral structure of
weak interactions, as well as setting extraordinary limits on
charged-lepton-flavor-violating processes. Measurements of the muon's anomalous
magnetic moment offer singular sensitivity to the completeness of the standard
model and the predictions of many speculative theories. Spectroscopy of muonium
and muonic atoms gives unmatched determinations of fundamental quantities
including the magnetic moment ratio $\mu_\mu / \mu_p$, lepton mass ratio
$m_{\mu} / m_e$, and proton charge radius $r_p$. Also, muon capture experiments
are exploring elusive features of weak interactions involving nucleons and
nuclei.
  We will review the experimental landscape of contemporary high-precision and
high-sensitivity experiments with muons. One focus is the novel methods and
ingenious techniques that achieve such precision and sensitivity in recent,
present, and planned experiments. Another focus is the uncommonly broad and
topical range of questions in atomic, nuclear and particle physics that such
experiments explore.
