We describe the influence of electromagnetism on the phenomenology of $K \to \pi\pi$ decays. This is required because the present data were analyzed without inclusion of electromagnetic radiative corrections, and hence contain several ambiguities and uncertainties which we describe in detail. Our presentation includes a full description of the infrared effects needed for a new experimental analysis. It also describes the general treatment of final state interaction phases, needed because Watson's theorem is no longer valid in the presence of electromagnetism. The phase of the isospin-two amplitude ${\cal A}_2$ may be modified by $50 \to 100\%$. We provide a tentative analysis using present data in order to illustrate the sensitivity to electromagnetic effects, and also discuss how the standard treatment of $\epsilon' /\epsilon$ is modified.