  The center-of-mass energies available at modern accelerators, such as the
Large Hadron Collider (LHC), and at forthcoming generation accelerators, such
as the Electron-Ion Collider (EIC), offer us a unique opportunity to
investigate hadronic matter under the most extreme conditions ever reached. In
particular, we can access the Regge-Gribov regime of QCD, described by the
Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach along with its non-linear
generalizations (the set of B-JIMWLK equations). The aim of these approaches is
to resum large-energy logarithmic corrections which spoil the convergence of
perturbative series at high-energy. The aforementioned approaches are
theoretically developed both in the leading (LL) and the next-to-leading (NLL)
approximation, but precise full NLL predictions still remains an open
challenge. Furthermore, extending BFKL beyond the NLL approximation has been an
open problem for more than twenty years. We face the task of hunting precision
in this field from different perspectives. In particular, within the BFKL
approach, we calculate the next-to-leading order (NLO) impact factor for the
Higgs boson production. This is the necessary ingredient to study the inclusive
forward emissions of a Higgs boson in association with a backward identified
jet. Moreover, by using already known NLO impact factors, we propose a series
of new semi-hard reactions that can be used to investigate BFKL dynamics at the
LHC within NLL accuracy. We consider also the problem of extending BFKL beyond
the NLL approximation and compute one of the ingredients entering the BFKL
kernel at the next-to-NLL (NNLL) accuracy. Finally, in the saturation
(non-linear) framework, we calculate the diffractive double hadron photo- or
electroproduction cross sections with full NLL accuracy, useful to detect
saturation effects, at both the future EIC or already at LHC (via Ultra
Peripheral Collisions).
