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This work is devoted, in the framework of cavity Quantum Electrodynamics, to the interaction of light with matter under an incoherent continuous pumping. As such, it describes physical systems like a quantum dot, that provides excitons (matter), inside a semiconductor microcavity, that provides photons (light). We unravel how the interplay between decay (losses of particles) and pumping (injection of particles) determines the physics of the half-light, half-matter particles that are realized in such systems. We study both weak and strong coupling, fermion and boson emitters, linear and nonlinear regimes, one quantum dot and many.