  In this review the quenching of the weak axial-vector coupling strength,
$g_{\rm A}$, is discussed in nuclear $\beta$ and double-$\beta$ decays. On one
hand, the nuclear-medium and nuclear many-body effects are separated, and on
the other hand the quenching is discussed from the points of view of different
many-body methods and different $\beta$-decay and double-$\beta$-decay
processes. Both the historical background and the present status are reviewed
and contrasted against each other. The theoretical considerations are tied to
performed and planned measurements, and possible new measurements are urged,
whenever relevant and doable. Relation of the quenching problem to the
measurements of charge-exchange reactions and muon-capture rates is pointed
out.
