Cardiovascular disease (CVD) is the leading cause of mortality worldwide and its incidence is rising due to an aging population. The development and progression of CVD is directly linked to adverse vascular hemodynamics and biomechanics, whose in-vivo measurement remains challenging but can be simulated numerically and experimentally. The ability to evaluate these parameters in patient-specific CVD cases is crucial to better predict future disease progression, risk of adverse events, and treatment efficacy. While significant progress has been made toward patient-specific hemodynamic simulations, blood vessels are often assumed to be rigid, which does not consider the compliant mechanical properties of vessels whose malfunction is implicated in disease. In an effort to simulate the biomechanics of flexible vessels, fluid-structure interaction (FSI) simulations have emerged as promising tools for the characterization of hemodynamics within patient-specific cardiovascular anatomies. Since FSI simulations combine the blood's fluid domain with the arterial structural domain, they pose novel challenges for their experimental validation. This paper reviews the scientific work related to FSI simulations for patient-specific arterial geometries and the current standard of FSI model validation including the use of compliant arterial phantoms, which offer novel potential for the experimental validation of FSI results.