Cardiovascular disease is one of the leading cause of death in humans, affecting millions of people worldwide. This motivates research in numerical approaches for personalized hemodynamics with the aim of improving early diagnosis, treatment and medical device design. In this context, cardiovascular models are experiencing an increasing recent interest, with the first FDA-approved technologies becoming successful companies, creating new demand for such tools and pushing forward their clinical adoption. However, deterministic analysis of cardiovascular flow is simply inadequate to provide an accurate characterization of the patient physiology and new stochastic approaches need to be developed to efficiently quantify the effects of uncertainty from various sources, e.g., errors and inconsistency in clinical measurements, histological variability in vascular tissue and operator-dependent anatomical segmentation. In this talk, recent efforts to quantify the confidence in predicted clinical indicators from personalized hemodynamic models will be discussed, starting with the construction of zero-, one- and three-dimensional representations of the cardiovascular system. I will discuss the use of parallel adaptive Markov chain Monte Carlo for estimating the parameters of reduced order compartmental models, and how improved estimators can be constructed from Bayesian updates at the compartment level. Approaches for uncertainty propagation will also be introduced using estimators constructed from a multi-resolution stochastic expansion of the quantities of interested as well as multilevel/multifidelity Monte Carlo estimators. Applications will be presented in the context of coronary artery disease, congenital heart disease and detection of pulmonary hypertension in patients with diastolic heart failure.