Given the extensive and routine use of cardiovascular devices, a major limiting factor to their success is the thrombotic rate that occurs. This poses direct risk to the patient and requires counterbalancing with anticoagulation and other treatment strategies, contributing additional risks. Developing a better understanding of the mechanisms of device-induced thrombosis to aid in device design and medical management of patients is critical to advance the ubiquitous use and durability. Thus, mathematical and computational modeling of device-induced thrombosis has received significant attention recently, but challenges remain. Additional areas that need to be explored include microscopic/macroscopic approaches, reconciling physical and numerical timescales, immune/inflammatory responses, experimental validation, and incorporating pathologies and blood conditions. Addressing these areas will provide engineers and clinicians the tools to provide safe and effective cardiovascular devices.