We consider the absorption of probe photons by electrons in the presence of an intense, pulsed, background field. Our analysis reveals an interplay between regularization and gauge invariance which distinguishes absorption from its crossing-symmetric processes, as well as a physical interpretation of absorption in terms of degenerate processes in the weak field limit. In the strong field limit we develop a locally constant field approximation (LCFA) for absorption which also exhibits new features. We benchmark the LCFA against analytical calculations and explore its regime of validity. Pulse shape effects are also investigated, as well as infrared and collinear limits of the absorption process.