A bicuspid aortic valve (BAV) is a congenital cardiac disorder where the valve consists of only two cusps instead of three in a normal tricuspid valve (TAV). Although 97% of BAVs include asymmetric cusps, little or no prior studies investigated the blood flow through physiological three-dimensional BAV and root. This study presents four fully coupled fluid-structure interaction (FSI) models, including native TAV, asymmetric BAV with or without a raphe and an almost symmetric BAV. The FSI simulations are based on coupled structural and fluid dynamics solvers that allow accurate modeling of the pressure load on both the root and the cusps. The partitioned solver has non-conformal meshes and the flow is modeled employing an Eulerian approach. The cusps tissue in the structural model is composed of hyperelastic finite elements with collagen fiber network embedded in the elastin matrix. The tissues behavior of the aortic sinuses is also hyperelastic. The coaptation is modeled with master-slave contact algorithm. A full cardiac cycle is simulated by imposing the same physiological blood pressure at the upstream and downstream boundaries, for all the TAV and BAV models. The latter have significantly smaller opening area compared to the TAV. Larger stress values were also found in the cusps of the BAV models with fused cusps, both at the systolic and diastolic phases. The asymmetric geometry cause asymmetric vortices and much larger wall shear stress on the cusps, which is a potential cause for early valvular calcification in BAVs.