  Unstable particles are notorious in perturbative quantum field theory for
producing singular propagators in scattering amplitudes that require
regularization by the finite width. In this review I discuss the construction
of an effective field theory for unstable particles, based on the hierarchy of
scales between the mass, M, and the width,Gamma, of the unstable particle that
allows resonant processes to be systematically expanded in powers of the
coupling alpha and Gamma/M, thereby providing gauge-invariant approximations at
every order. I illustrate the method with the next-to-leading order line-shape
of a scalar resonance in an abelian gauge-Yukawa model, and results on NLO and
dominant NNLO corrections to (resonant and non-resonant) pair production of
W-bosons and top quarks.
