  I present results from the first lattice QCD calculations of axial-current
matrix elements in light nuclei, performed by the NPLQCD collaboration.
Precision calculations of these matrix elements, and the subsequent extraction
of multi-nucleon axial-current operators, are essential in refining theoretical
predictions of the proton-proton fusion cross section, neutrino-nucleus cross
sections and $\beta\beta$-decay rates of nuclei. In addition, they are expected
to shed light on the phenomenological quenching of $g_A$ that is required in
nuclear many-body calculations.
