  Recently, the BESIII collaboration has reported numerous measurements of
various $D_{(s)}$ meson semileptonic decays with significantly improved
precision. Together with similar studies carried out at BABAR, Belle, and CLEO,
new windows to a better understanding of weak and strong interactions in the
charm sector have been opened. In light of new experimental data, we review the
theoretical description and predictions for the semileptonic decays of
$D_{(s)}$ to a pseudoscalar or a vector meson. This review is essentially an
extended discussion of our recently published results obtained in the framework
of the covariant confining quark model.
