We have seen in the last decades an enormous effort from the
experimental side to measure numerous physical observables and an
equally important effort from the Theory community to provide
phenomenological predictions for comparison. In this talk, we will
focus on two topics which are relevant for LHC phenomenology.
(I) We generally use perturbation theory to compute cross-sections,
with αs (the strong coupling) as the small expansion parameter. At
very high energies, the convergence of the perturbative expansion
--which is truncated at a certain order in αs-- is not a priori
guaranteed. This is because large logarithms in energy appear in
Feynman diagrams to all orders and they need to be resummed properly.
We will present examples of recent phenomenological studies where the
use of advanced Monte Carlo techniques takes care of the resummation.
The Reggeon, Pomeron and Odderon will be introduced in a friendly,
pedagogical manner.
(II) In the second part of the talk, after a short survey of
state-of-the-art techniques for the calculation of radiative
corrections, we will introduce the Loop-Tree duality method for
particle physics phenomenology. This is an approach which allows the
computation of cross-sections beyond the tree-level by treating real
and virtual radiative corrections on equal footage. We will give a
status report of our numerical implementation of the method and we
will present non-trivial examples.