By placing an organic semiconductor material having a relatively narrow electronic transition into an optical microcavity, it is possible to 'mix' excitons with confined cavity photons, forming states termed 'cavity polaritons'. Here, I discuss the formation of polariton states in microcavities containing J-aggregates of two different molecular dyes (cyanine dyes), whose J-band electronic transitions are both coupled to the same cavity photon mode. Under such conditions, three polariton branches are formed, with the "middle" polariton branch composed of an admixture of the cavity photon and the two different exciton states. I show using both photoluminescence excitation spectroscopy and photoluminescence emission measurements that such "hybrid" polariton states effectively act as an energy transfer pathway, allowing energy to be transferred between the different exciton states. A model is presented that describes exciton scattering into polariton states, and the subsequent decay and energetic relaxation of polaritons. I argue that the transfer of middle-branch polaritons to the lower-lying excitonic states is an efficient process, that occurs in time-scale of less than 10 fs. I then discuss structures in which a single J-aggregated cyanine dye is placed into a microcavity in which the extended cavity path-length results in the formation of a series of closely spaced cavity photon modes. It is shown that excitons in the cavity can simultaneously undergo strong coupling with at least four cavity photon-modes, effectively forming a ladder of polariton states, with a significant polariton population found in 3 adjacent polariton branches.