  The present work reviews the various aspects of the extension of the
large-$N_c$ approach, as had been proposed and developed by 't Hooft, to the
case of tetraquark states, which are a category of the general class of exotic
states, also called multiquark states, whose internal valence-quark structure
does not match with that of ordinary hadrons, and which have received, in
recent years, many experimental confirmations. The primary question of
describing, or probing, on theoretical grounds, multiquark states is first
examined. The signature of such states inside Feynman diagrams in relation with
their singularities is highlighted. The main mechanisms of formation of
tetraquark states, provided by the diquark model and the molecular scheme, are
considered together with their specific implications. The properties of
tetraquark states at large $N_c$ are analyzed through the Feynman diagrams that
describe two-meson scattering amplitudes. It turns out that, in that limit, the
possible formation of tetraquark states is mainly due to the mutual
interactions of their internal mesonic clusters. These essentially arise from
the quark-rearrangement, or quark-interchange, mechanism. In coupled-channel
meson-meson scattering amplitudes, one may expect the occurrence of two
independent tetraquark states, each having priviledged couplings with the two
mesons of their dominant channel. The question of the energy balance of various
schemes in the static limit is also analyzed. The clarification of the
mechanisms that are at work in the formation of tetraquarks is the main outcome
from the large-$N_c$ approach to this problem.
