Title: Precision measurements of G_F and g_P with muons. Abstract: Two of a new generation of muon lifetime experiments will be described. The first, MuLAN, measures the positive muon lifetime and provides the most precise determination of the Fermi constant G_F, a basic parameter that sets the strength of the weak interaction. The second, MuCap, measures the negative muon lifetime in ultrapure hydrogen gas. The shorter lifetime of the negative muon compared to that of the positive muon is attributable to an additional disappearance mechanism, capture on the proton. Muon capture on the proton is sensitive to the weak pseudoscalar form factor g_P, one of the parameters characterizing the nucleon electroweak charged-current interaction. There is a precise theoretical prediction for g_P based on chiral symmetry of QCD, yet the results of past experiments are controversial: they are dependent on a poorly-known, mu-molecular kinetic parameter, and there is no point of mutual agreement between theory and all experiments. The situation was clarified last summer with the publication of first physics results from the MuCap experiment, which determined g_P precisely and unambiguously.