Our insight into the pathogenesis of cholestatic liver disease remains limited, partly owing to challenges in capturing the multitude of factors that contribute to disease pathogenesis in vitro. Tissue engineering could address this challenge by combining cells, materials and fabrication strategies into dynamic modelling platforms, recapitulating the multifaceted aetiology of cholangiopathies. Herein, we review the advantages and limitations of platforms for bioengineering the biliary tree, looking at how these can be applied to model biliary disorders, as well as exploring future directions for the field.