  The class of semi-hard reactions represents a promising venue where to
enhance our knowledge of strong interactions and deepen the aspects related to
this theory in kinematical regimes so far unexplored. In particular, the high
energies reached in electron-proton and in proton-proton collisions first at
HERA and then at the LHC, allow us to study scattering amplitudes of hard and
semi-hard processes in perturbative QCD. The structure of this thesis can be
considered twofold. On one hand, the possibility to distinguish those channels
where at least two final-state particles are emitted with large separation in
rapidity and with an untagged system, permits to test the BFKL dynamics as
resummation energy logarithms in the $t$-channel. In the BFKL formalism, the
Mueller--Navelet jets process has been one of the most investigated reactions.
With the idea of deepening our understanding of the BFKL approach, a new
channel is proposed: the inclusive production of a light charged hadron and a
jet with high transverse momentum widely separated in rapidity. The importance
of this process relies in the possibility to probe a complementary region to
one analyzed for the Mueller--Navelet jets. Additionally, another reaction is
proposed: the heavy-quark pairs hadroproduction. On the other hand, also the
class of processes featured by the detection of a single forward object in
lepton-proton collision offers the opportunity to develop intriguing
phenomenological studies. In particular, the exclusive leptoproduction of light
vector mesons, $\rho$ and $\phi$, is exhaustively investigated. In this
context, the study of helicity-dependent observables allows us to discriminate
among several unintegrated gluon distribution models, whose original definition
naturally encodes the BFKL-equation evolution dynamics. This kind of parton
density allows us to get access to the hadronic structure at small-$x$.
