This paper reviews the techniques developed jointly by Rolls-Royce Bristol and Oxford University for determining detailed heat transfer coefficient distributions inside turbine blade and vane cooling passages. These techniques make use of a low temperature phase change paint to map the heat flux distributions within models of the cooling passages. The paints change from an opaque coating to a clear liquid at a well defined melting point. Thus, the surface temperature history of a model subjected to transient convective heating is recorded. From this history the heat transfer coefficient distribution is deduced using a transient conduction analysis within the model. The general method may be applied to a range of model thicknesses and geometries. The Rolls-Royce data are usually obtained from the inner surface of thick walled models whereas the Oxford measurements are performed on the outside of thin walls. Results are presented for the detailed heat transfer coefficient distributions within a variety of cooling passages. Firstly, smooth ducts of circular cross section are considered and serve the purpose of validating the experimental techniques. Secondly, results for complex passages with varying cross-sectional area are presented, and the effect of introducing discrete roughness elements and film cooling exhausts into these ducts assessed. Finally, data obtained from a comprehensive examination of a typical engine multi-pass cooling geometry are presented.