Plastic pollution has been observed throughout the world's oceans and estuaries whether floating at the surface, settled in bottom sediments, washed up on beaches, or ingested by marine life. However, the vast majority of discarded plastics are unaccounted for. The problem of predicting the fate of discarded plastics has spurred fundamental research into fluid-particle interactions in previously unexplored regimes. Through talks and focused discussion groups taking place during a February 2022 online workshop hosted by the Banff International Research Station (BIRS), theorists, experimentalists, numerical modellers and observational oceanographers presented recent advances and identified outstanding problems in predicting plastic transport in the ocean, focusing on the role of fluid dynamics. The outcomes of this meeting and discussions that followed are reported upon here.