Global plastic pollution in the environment is of widespread concern. Rivers have been recognised as an important transport pathway, leading to the spatial redistribution of land-based plastic, and as a key source of plastic in the world’s oceans. Several global models have been developed to estimate the transport, accumulation and export of plastics into the ocean. Many, if not all, of these attempts formulate the river plastic transport dynamics based on estimates of land-based plastic pollution and river discharge. However, the direct relationship between discharge and the river plastic flux is put into question by river plastic pollution observations, which have largely failed to obtain any significant correlation between discharge and the plastic flux at non-extreme discharge levels. Here, we seek to explain these counterintuitive findings and provide a new perspective on how the riverine plastic research and models could improve. We address this by separating the driving forces of plastic transport into the transport capacity (transport), and the potential plastic load (supply). This perspective provides an explanation of the absence of generalizable correlations between discharge and the riverine plastic flux observations. We also highlight the need to broaden the focus of plastic research to include not only the flux in the river, but also the current plastic stocks and fluxes of the whole river systems and their relationship to human behaviour.