Unitarity and Analyticity of scattering amplitudes,
when combined with Cauchy's Residue Theorem and its multivariate
generalizations via Stokes' Theorem, turn into powerful techniques for
evaluating radiative corrections.
In the context of the by-now known as unitarity-based methods,
I shall review how the simple implementation of complex momenta
for propagating particles enable us to carry out the calculation of
tree-level and one-loop amplitudes very efficiently,
and to provide, as well, the Optical Theorem with a geometrical
interpretation as a Berry's phase.
Together with analytic techniques, I shall discuss also SAMURAI,
a seminumerical implementation of unitarity-based methods.
