Gas turbine engines are extensively used in the aviation and power generation industries. They are used as topping cycles in combined cycle power plants, or as stand alone power generation units. Gains in thermodynamic efficiency can be realized by increasing the turbine inlet temperatures. Since modern turbine inlet temperatures exceed the melting point of the constituent superalloys, it is necessary to provide an aggressive cooling system. Relatively cool air, ducted from the compressor of the engine is used to remove heat from the hot turbine blade. This air flows through passages in the hollow blade (internal cooling), and is also ejected onto the surface of the blade to form an insulating film (film cooling). Modern land-based gas turbine engines use high Reynolds number internal flow to cool their internal passages. The first part of this study focuses on experiments pertaining to passages with Reynolds numbers of up to 400,000. Common turbulator designs (45degree parallel sharp-edged and round-edged) ribs are studied. Older correlations are found to require corrections in order to be valid in the high Reynolds number parameter space. The effect of rotation on heat transfer in a typical three-pass serpentine channel is studied using a computational model with near-wall refinement. Results from this computational study indicate that the hub experiences abnormally high heat transfer under rotation. An experimental study is conducted at Buoyancy numbers similar to an actual engine on a wedge shaped model trailing edge, roughened with pin-fins and equipped with slot ejection. Results show an asymmetery between the leading and trailing surfaces due to rotation - a difference which is subdued due to the provision of pin-fins. Film cooling effectiveness is measured by the PSP mass transfer analogy technique in two different configurations: a flat plate and a typical high pressure turbine blade. Parameters studied include a step immediately upstream of a row of holes; the Strouhal number (quantifying rotor-stator interaction) and coolant to mainstream density ratio. Results show a deterioration in film cooling effectiveness with on increasing the Strouhal number. Using a coolant with a higher density results in higher film cooling effectiveness.