  We study relaxation and dephasing in a strongly driven two-level system
interacting with its environment. We develop a theory which gives a
straightforward physical picture of the complex dynamics of the system in terms
of dressed states. In addition to the dressing of the energy diagram, we
describe the dressing of relaxation and dephasing. We find a good quantitative
agreement between the theoretical calculations and measurements of a
superconducting qubit driven by an intense microwave field. The competition of
various processes leads to a rich structure in the observed behavior, including
signatures of population inversion.
