Conjugated polymer nanoparticles are a class of nanoparticles with many useful and interesting properties, including very high fluorescence brightness, excellent photostability, and sensing capabilities. They also exhibit interesting and potentially useful phenomena, such as highly efficient energy transfer, anomalous single particle blinking, and twinkling phenomena associated with polaron motion. As little as one dye molecule per nanoparticle can efficiently quench the fluorescence of hundreds of polymer chromophore units. Similarly, loss of a single electron can result in quenching of hundreds of chromophores. These phenomena and properties are dictated by the nature of interactions between chromophores in this dense, nanoscale multichromophoric system, and are characterized as amplified energy transfer or multiple energy transfer. In this review, we summarize the key aspects of conjugated polymer nanoparticles optical properties and phenomena, and discuss the current understanding of exciton dynamics in these and related systems. In particular, our current understanding and theoretical models for amplified or multiple energy transfer based on exciton theory and Förster resonance energy transfer are explored.