  In this talk, we review the basis of the loop-tree duality theorem, which
allows to rewrite loop scattering amplitudes in terms of tree-level like
objects. Since the loop measure is converted into a phase-space one, both
virtual and real contributions are expressible using the same integration
variables. A physically motivated momentum mapping allows to generate the real
emission process starting from the Born kinematics and the loop momenta. The
integrand-level combination leads to regular functions, which can be integrated
without using dimensional regularization (DREG) and correctly reproduce the
finite higher-order corrections to physical observables. We explain the
implementation of this novel approach to compute some benchmark physical
processes, and we show how to deal with both infrared and ultraviolet
divergences in four space-time dimensions.
