The interaction of organic molecules and molecular aggregates with electromagnetic fields that are strongly confined inside optical cavities within nanoscale volumes, has allowed the observation of exotic quantum regimes of light-matter interaction at room temperature, for a wide variety of cavity materials and geometries. Understanding the universal features of such organic cavities represents a significant challenge for theoretical modelling, as experiments show that these systems are characterized by an intricate competition between coherent and dissipative processes involving entangled nuclear, electronic and photonic degrees of freedom. In this review, we discuss a new theoretical framework that can successfully describe organic cavities under strong light-matter coupling. The theory combines standard concepts in chemical physics and quantum optics to provide a microscopic description of vibronic organic polaritons that is fully consistent with available experiments, and yet is profoundly different from the common view of organic polaritons. We show that by introducing a new class of vibronic polariton wave functions with a photonic component that is dressed by intramolecular vibrations, the new theory can offer a consistent solution to some of the long-standing puzzles in the interpretation of organic cavity photoluminescence. Throughout this review, we confront the predictions of the model with spectroscopic observations, and describe the conditions under which the theory reduces to previous approaches. We finally discuss possible extensions of the theory to account for realistic complexities of organic cavities such spatial inhomogeneities and the multi-mode nature of confined electromagnetic fields.
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