The advent of attosecond science, with main objectives to probe and to control ultrafast dynamics in quantum systems, brought in the past few years a fresh look on photoemission. This very fundamental process was indeed recently revisited in the time domain, in a series of pioneering experiments that were soon accompanied by an intense theoretical activity devoted to the interpretation of the reported "photoemission delays". At the conference, we will present some contributions of our group to this topic, with a focus on the characterization of photoemission dynamics in terms of "scattering delay" and "transition delay" as evidenced in numerical experiments performed on simple model systems.