Virtual Corrections to Bremsstrahlung in High-Energy Collider Physics: LHC and $e^+ e^-$ Colliders

We describe radiative corrections to bremsstrahlung and their application to high energy collider physics, focusing on the applications to luminosity measurement, fermion pair production and radiative return. We review the status of one loop radiative corrections in BHLUMI and the KKMC, including cross checks with newer results developed independently for radiative return. We outline a YFS-exponentiated approach to the Drell-Yan process for LHC physics, including a discussion of the relevant radiative corrections.