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.