Electronic excitations in small aggregates, thin films, and crystals of conjugated organic molecules play a fundamental role in the operation of a wide array of organic-based devices including solar cells, transistors, and light-emitting diodes. Such excitations, or excitons, are generally spread out over several molecules: a balance between the delocalizing influence of resonant intermolecular coupling and the localizing influence of static and dynamic disorder determines the coherence range of the exciton. Because of the "soft" nature of organic materials, significant nuclear relaxation in the participating molecules also accompanies the electronic excitations. To properly understand energy or charge transport, one must treat intermolecular (excitonic) coupling, electron-vibrational coupling, and disorder on equal footing. In this Account, we review the key elements of a theoretical approach based on a multiparticle representation that describes electronic excitations in organic materials as vibronic excitations surrounded by a field of vibrational excitations. Such composite excitations are appropriately called Frenkel excitonic polarons. For many conjugated molecules, the bulk of the nuclear reorganization energy following electronic excitation arises from the elongation of a symmetric vinyl stretching mode with energy approximately 1400 cm(-1). To appreciate the impact of aggregation, we study how the vibronic progression of this mode, which dominates the isolated (solvated) molecule absorption and emission spectra, is distorted when molecules are close enough to interact with each other. As we demonstrate in this Account, the nature of the distortion provides a wealth of information about how the molecules are packed, the strength of the excitonic interactions between molecules, the number of molecules that are coherently coupled, and the nature of the disorder. We show that the aggregation-induced deviations from the Poissonian distribution of vibronic peak intensities take on two extremes identified with ideal H- and J-aggregates. The sign of the nearest neighbor electronic coupling, positive for H and negative for J, distinguishes the two basic aggregate forms. For several decades, researchers have known that H-aggregates exhibit blue-shifted absorption spectra and are subradiant while J-aggregates exhibit the opposite behavior (red-shifted absorption and superradiance). However, the exact inclusion of exciton-vibrational coupling reveals several more distinguishing traits between the two aggregate types: in H(J)-aggregates the ratio of the first two vibronic peak intensities in the absorption spectrum decreases (increases) with increasing excitonic coupling, while the ratio of the 0-0 to 0-1 emission intensities increases (decreases) with disorder and increases (decreases) with increasing temperature. These two extreme behaviors provide the framework for understanding absorption and emission in more complex morphologies, such as herringbone packing in oligo(phenylene vinylene)s, oligothiophenes and polyacene crystals, as well as the polymorphic packing arrangements observed in carotenoids.