  Heavy-flavored emissions have been always considered as an excellent channel
to test properties of Quantum chromodynamics (QCD) at present and future
colliders. Among different regimes, in which heavy-flavor production can be
investigated, we focus our attention on the semi-hard one, where $s \gg \{ Q^2
\} \gg \Lambda_{QCD}$ ($s$ is the squared center-of-mass energy, $\{ Q^2 \}$ a
(set of) hard scale(s) characteristic of the process and $\Lambda_{QCD}$ the
QCD mass scale). Here, we build predictions in a hybrid collinear/high-energy
factorization, in which the standard collinear description is supplemented by
the Balitsky-Fadin-Kuraev-Lipatov resummation of large energy logarithms. The
definition and the study of observables sensitive to high-energy dynamics in
the context of heavy-flavor physics has the double advantage of (i) allowing to
get a stabilization of the BFKL series under higher-order corrections and (ii)
providing us with an auxiliary tool to investigate heavy-flavor production in
wider kinematical ranges. Hence, we propose a scientific program on
heavy-flavor physics at high-energy with the goal of considering both open
(heavy-jet) and bound states ($\Lambda$ baryons, heavy-light mesons and
quarkonia).
