Respiratory syncytial virus (RSV) is a leading cause of acute lower respiratory tract infection in young children and the second leading cause of infant death worldwide. While global circulation has been extensively studied for respiratory viruses such as seasonal influenza, and more recently also in great detail for SARS-CoV-2, a lack of global multi-annual sampling of complete RSV genomes limits our understanding of RSV molecular epidemiology. Here, we capitalise on the genomic surveillance by the INFORM-RSV study and apply phylodynamic approaches to uncover how selection and neutral epidemiological processes shape RSV diversity. Using complete viral genome sequences, we show similar patterns of site-specific diversifying selection among RSVA and RSVB and recover the imprint of non-neutral epidemic processes on their genealogies. Using a phylogeographic approach, we provide evidence for air travel governing the global patterns of RSVA and RSVB spread, which results in a considerable degree of phylogenetic mixing across countries. Our findings highlight the potential of systematic global RSV genomic surveillance for transforming our understanding of global RSV spread.