We discuss the equilibrium and out of equilibrium dynamics of cavity QED in presence of dissipation beyond the standard perturbative treatment of losses. Using the dynamical polaron emph{ansatz} and Matrix Product State simulations, we discuss the case where both light-matter $g$-coupling and system-bath interaction are in the ultrastrong coupling regime. We provide a critical $g$ for the onset of Rabi oscillations. Besides, we demonstrate that the qubit is emph{dressed} by the cavity and dissipation. That such dressing governs the dynamics and, thus, it can be measured. Finally, we sketch an implementation for our theoretical ideas within circuit QED technology.
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