Optical emission of laser-produced plasmas from solids, liquids, and gases, from their fundamentals to their potential applications, has been comprehensively reported in multiple research manuscripts, reviews, and books. There are nevertheless enough serious unanswered issues and questions still present on what at first sight seemed to be much easier, the laser-induced breakdown spectroscopy (LIBS) of organic compounds. Ideally, for all organic molecules, one would expect homologous emission spectra, differing only in the presence or absence of signals associated to the containing elements and their intensity relative to their content. Yet, the reality is much more complex. In laser-induced plasmas of organic compounds, a broad variety of species may be formed depending on the irradiation parameters. Furthermore, there is not a uniform breakage for all the molecules constituting the ablated mass. At once, the plasma is a dynamic entity per se, which implies that the spatial distribution of each species in the source plasma is different. In addition, multiple circumstances and mechanisms may contribute to the extinction of some species and the formation of new ones. Thus, the surrounding atmosphere where the plasma evolves and the time elapsed from its formation also have a strong influence on the spectral signature gathered. In essence, any change in any of the variables involved in the cycle of an organic plasma, from those causing its formation to those governing its expansion, defines a new scenario that lead to a different LIBS spectrum for a same organic compound. The present paper reviews the common emitting species populating the laser plasmas of organic compounds, the routes to their formation, mostly those related to the production of diatomic radicals, the dynamics of such species, in space and time, and the physical parameters that they confer to the plasma. Concurrently, the influence that the structures of the molecular solids and the set of excitation variables may exert on the optical emissions observed is also discussed. Finally, some details on the modeling of organic plasmas are provided.