Abstract: Computational Fluid Dynamics (CFD) plays a significant role in the industrial design of gas turbine components. The desire for higher thermal efficiencies has steadily increased the turbine inlet temperature putting very stringent requirements on materials and on blade cooling technologies in the high-pressure turbine section to do more with less coolant mass flow rates. Both internal and external cooling is utilized. While internal cooling protects the first stage nozzle vain and blade through internal cooling channels, external cooling is mostly through injection of coolant through discrete hole injection on the blade surface. A wide variety of geometries and techniques are used in internal cooling ranging from serpentine channels to double-walled blades equipped with turbulence generators ranging from ribs of different configurations, pin fins, protrusions, dimples, impinging jets, etc. The intricate geometry of high-pressure turbine blades coupled with complex external and internal turbulent flow makes accurate thermal predictions of blade metal temperatures a grand challenge. Amongst the different fidelity models available, unsteady methods based on the principles of Large-Eddy Simulations (LES) when combined with high performance parallel computing show promise. LES and other unsteady methods instill better predictability but are much more expensive than Reynolds-Averaged Navier-Stokes Simulations (RANS). Unsteady methods because of their high computational complexity mandate the use of parallel computing on modern high performance computing (HPC) architectures. Supercomputing has evolved from single processor vector units in the early 90's to hundreds of thousands of processing units with complex hierarchical memory sub-systems exhibiting different bandwidths and latencies, which need to be recognized by the application for effective use. The lecture will describe the challenges in predicting turbine blade heat transfer and in the adaptation of modern HPC architectures and programming models to CFD. The lecture will elaborate on progress made in the last two decades and opportunities for advancing prediction capability by using techniques and methods from CFD mapped effectively to modern HPC architectures for high performance and reduced turnaround times.