  The singlet capture rate $\Lambda_S$ for the semileptonic weak process $\mu+p
\to n+\nu_\mu$ has been measured in the MuCap experiment. The novel
experimental technique is based on stopping muons in an active target,
consisting of a time projection chamber operating with ultra-pure hydrogen.
This allows the unambiguous determination of the pseudoscalar form factor $g_P$
of the charged electroweak current of the nucleon. Our first result
$g_P(q^2=-0.88 m^2_\mu) = 7.3 \pm 1.1 $ is consistent with accurate theoretical
predictions and constitutes an important test of QCD symmetries. Additional
data are being collected with the aim of a three-fold reduction of the
experimental uncertainties. Building on the developed advanced techniques, the
new MuSun experiment is being planned to measure the muon capture rate on the
deuteron to 1.5% precision. This would provide the by far most accurate
experimental information on the axial current interacting with the two-nucleon
system and determine the low energy constant $L_{1A}$ relevant for solar
neutrino reactions.
  Muon induced atomic and molecular processes represent challenges as well as
opportunities for this science program, and their interplay with the main
nuclear and weak-interaction physics aspects will be discussed.
