  The successful precision measurement of the rate of muon capture on a proton
by the MuCap Collaboration allows for a stringent test of the current
theoretical understanding of this process. Chiral perturbation theory, which is
a low-energy effective field theory that preserves the symmetries and the
pattern of symmetry breaking in the underlying theory of QCD, offers a
systematic framework for describing $\mu p$ capture and provides a basic test
of QCD at the hadronic level. We describe how this effective theory with no
free parameters reproduces the measured capture rate. A recent study has
addressed new sources of uncertainties that were not considered in the previous
works, and we review to what extent these uncertainties are now under control.
Finally, the rationale for studying muon capture on the deuteron and some
recent theoretical developments regarding this process are discussed.
