Improved computational fluid dynamics tools based on Reynolds-averaged NavierStokes (RANS) equations have shown that the behavior of simple flow cases can be predicted with a reasonable degree of accuracy. Their predictive capability, however, substantially diminishes whenever major secondary vortices, adverse pressure gradients, and wake-boundary layer interactions are present. Flow through high-pressure (HP) turbine components uniquely incorporates almost all of the above features, interacting with each other and determining the efficiency and performance of the turbine. Thus, the degree of accuracy of predicting the flow through a HP turbine can be viewed as an appropriate benchmark test for evaluating the predictive capability of any RANS-based method. Detailed numerical and experimental investigations of different HP turbines presented in this paper have revealed substantial differences between the experimental and the numerical results pertaining to the individual flow quantities. This paper aims at identifying the quantities whose simulation inaccuracies are pre-eminently responsible for the aforementioned differences. This task requires (a) a meticulous experimental investigation of all individual thermofluid quantities and their interactions resulting in an integral behavior of the turbomachine in terms of efficiency and performance, (b) a detailed numerical investigation using appropriate grid densities based on simulation sensitivity, and (c) steady and transient simulations to ensure their impact on the final numerical results. To perform the above experimental and numerical tasks, two different HP turbines were investigated: (1) a two-stage turbine with moderately compound-leaned stator blades and (2) a three-stage turbine rotor with compound-leaned stator and rotor blades. Both turbines have been thoroughly measured and numerically simulated using RANS and URANS. Detailed interstage radial and circumferential traversing presents a complete flow picture of the second stage. Performance measurements were carried out for design and off-design rotational speeds. For comparison with numerical simulations, the turbines were numerically modeled using a commercially available code. An extensive mesh sensitivity study was performed to achieve a grid-independent accuracy for both steady and transient analysis. Comparison of RANS/URANS results with the experimental ones revealed differences in total pressure for the two-stage turbine of up to 5%. A significantly lower difference of less than 0.2% is observed for the three-stage turbine with specially designed blades to suppress the secondary flow losses. Analyzing the physical background of a RANS-based solver, it was argued that the differences of individual quantities exhibited in the paper were attributed to the deficiencies in dissipation and transition models.