  In this review we present and discuss the determination of the magnitude of
the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameter $V_{cb}$. The CKM matrix
parametrizes the weak charged current interactions of quarks in the Standard
Model (SM), and a precise determination of its elements has always been one of
the most important targets of particle physics. The precise knowledge of the
$|V_{cb}|$ value plays a pivotal role in testing the flavour sector of the SM
and in the analyses of the unitarity of the CKM matrix. The SM does not predict
the values of the CKM matrix elements, which have to be extracted by
experimental data. Given the variety of channels that allow the extraction of
$|V_{cb}|$, different theoretical and experimental techniques are mustered for
the $|V_{cb}|$ determination. The exertion toward precision represents not only
a significant test of our theoretical procedures but a stimulus towards better
detection performances. The most precise measurements of $|V_{cb}|$ come from
semileptonic decays, that being tree level at the lowest order in the SM are
generally considered unaffected by physics beyond the SM.
  After summarizing the characteristics of the SM that set the frame for the
determination of $|V_{cb}|$, we discuss inclusive and exclusive semileptonic
$B$ decays. We analyze the $|V_{cb}|$ extraction methods and recent results,
detailing both the theoretical and experimental techniques, and, finally,
outline future prospects. We also comment on exclusive decays into heavy
leptons, on the observables $R(D)$ and $R(D^\ast)$, on decays to excited $D$
meson states and on baryon decays.
