Scientific advances and several technical breakthroughs have led to a remarkable increase in available laser intensities over the past decades. In available ultra-intense laser fields, photon fluxes may become so high that free charge carriers interact coherently with several of the field's photons. In this thesis such nonlinear interactions are investigated for the prime example of radiation emission by electrons scattered from intense laser pulses of arbitrary temporal structure. To this end, nonlinear quantum field theory is employed taking the interaction with the laser into account...