Although blood-contacting medical devices are used widely, blood clot formation (thrombosis) leads to device failure and potentially catastrophic adverse thrombotic events for patients, such as stroke or pulomonary embolism. Systemic anti-thrombotic drugs aimed at reducing these complications do not always prevent device thrombosis and can cause increased bleeding risks. Therefore, our understanding of material thrombosis mechanisms needs to be improved in order to develop next generation blood-contacting medical devices and materials. Medical device development requires material thrombogenicity evaluation according to the International Standards 10993-4 Biological evaluation of medical devices-Selection of tests for interactions with blood, which highlights that one of the key aspects for testing is a clinically relevant flow system. In this review, we first provide an overview of the current knowledge regarding material thrombosis and important physical and biological aspects of blood flow in relation to thrombus formation. We then examine commonly used in vitro flow systems to evaluate material and medical device thrombosis, focusing on their capabilities, advantages and disadvantages. Finally, we explore recent advances in technology that will aid in improving the design and fabrication of flow systems, mechanistic analysis and computational modelling.