Semi-inclusive deep inelastic scattering (SIDIS) is one of the key processes to extract transverse momentum dependent parton distributions (TMDs). An advantage of electrons is that they are much cleaner probes of nucleon structure than hadron beams, but, at the same time, electron scattering at large momentum transfer can be a source of considerable photon radiation, which can significantly distort the inferred nucleon structure. In this talk, I will present a new factorized approach to SIDIS, treating QED and QCD radiation on equal footing and providing a systematically improvable approximation to the extraction of TMDs. I will show how radiation effects prevent a well-defined ``photon-hadron'' frame, forcing one to use a two-step process to account for the radiation, and demonstrate how the QED contributions can be well approximated by collinear factorization. I will illustrate the utility of the new method by explicit application to transverse single spin asymmetries.