<p>Current in silico dialyser models remain accurate only under narrowly constrained conditions. Advances in computing power and increasing levels of interdisciplinary collaboration, however, now set the stage for more robust computational haemodialyser models. In this review, we survey existing modelling approaches—long used to guide haemodialyser design and clinical nephrology practice—identify key unresolved challenges, and propose computational strategies poised to accelerate the development of dialyser technologies that better meet the needs of kidney failure patients.</p>