Pump-probe techniques with high temporal resolution allow one to drive a system of interest out of equilibrium and at the same time, probe its properties. Recent advances in these techniques open the door to studying new, non-equilibrium phenomena such as Floquet topological insulators and superconductors. These advances also necessitate the development of theoretical tools for understanding the experimental findings and predicting new ones. In the present work, we provide a theoretical foundation to understand the non-equilibrium behavior of a Dirac system. We present detailed numerical calculations and simple analytic results for the evolution of a Dirac system irradiated by light. These results are framed intuitively by appealing to the recently revitalized notion of side-bands. We find that, under the application of circularly polarized light, a Dirac point only ever splits into two copies of sidebands. Meanwhile, the application of linearly polarized light leaves the Dirac point intact while producing side bands. Our immediate interest in this work is in connection to time and angle resolved photoemission experiments, where we find excellent qualitative agreement between our results and those in the literature. However, our results are general and may prove useful beyond this particular application and should be relevant to other pump-probe experiments.