Schistosomes experience many populational selection pressures but their sexual and reproductive biology are unusually dynamic and particularly special. If given sufficient opportunity, certain schistosome species can hybridize and give rise to progeny that have either abrupt genomic changes or exhibit more gradual genetic introgressions. The importance and impact of such short- and long-term dynamics were discussed and debated in February 2025 at The Royal Society, with the 12 resultant papers elaborated upon here. Schistosomes were discovered just under 175 years ago and continue to attract global attention, being interlinked in several dimensions of the Sustainable Development Goals. Adult schistosomes are dioecious helminths and parasitize a wide range of mammals; hundreds of millions of people, and innumerable livestock, have schistosomiasis. This disease raises their medical and veterinary importance, notwithstanding their detrimental economic impact. Once their lifecycle was elucidated, involving certain freshwater snail species, public health interventions could be waged. Attack points were developed, with health education and safe water hygiene applied, sometimes with local snail control, but effective constraint was only achieved once praziquantel, a relatively low-cost anthelminthic medicine, was procured then administered at scale. As praziquantel is active against adult worms alone, protective effects are short-term and retreatment is required. This article is part of the Science+ meeting issue ‘Parasite evolution and impact in action: exploring the importance and control of hybrid schistosomes’.