We reviewed 15 572 Australian species-level records of the marine planktonic dinoflagellate Tripos Bory (formerly Ceratium Schrank, a genus now restricted to freshwater species). The genus is represented by over 50 species and numerous varieties and forms in Australian tropical, subtropical and temperate marine waters and the Southern Ocean. There exists considerable plasticity in the morphology of many species, which has confounded species delimitations and created uncertainty around their spatial distributions. We newly illustrate by light and electron microscopy the rarely reported Tripos hundhausenii (Schröd.) Hallegr. & Huisman comb. nov. first described from the Arabian Sea, but increasingly being observed in Sydney coastal waters. A large number of Tripos species are widely distributed in temperate, subtropical and tropical waters and their distributions have remained remarkably stable in Australian waters over the past 60–80 years. By contrast, we identified a narrow group of warm-water species, including T. belone (Cleve) F.Gómez, T. cephalotus (Lemmerm.) F.Gómez, T. dens (Ostenf. & E.J.Schmidt) F.Gómez, T. digitatus (F.Schütt) F.Gómez, T. gravidus (Gourret) F.Gómez, T. incisus (G.Karst.) F.Gómez, T. paradoxides (Cleve) F.Gómez and T. praelongus (Lemmerm.) F.Gómez, that are commonly encountered off Sydney, rarely found down to Eden and Batemans Bay or Bass Strait, but occasionally occur as far south as King Island and Maria Island, Tasmania. These rare tropical Tripos species are carried southward by the East Australian and Leeuwin Currents and deserve careful attention in monitoring for future range expansions, changes in seasonality or upwelling or incursion of deep tropical waters.