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).