The paper reviews experimental and computational research directed at improving the internal cooling of gas-turbine blades. While not the most glamorous area of gas-turbine aerothermodynamics, the improvements in overall thermal efficiency directly attributable to internal blade cooling arguably outstrip those achieved in any other area of jet-engine research. The cooling arrangements within a blade adopt three cooling strategies: impinging leading-edge jets, serpentine passages for the mid-blade section, and pin fins near the trailing edge. Progress in each of these areas is examined. Although, in the second of these areas, CFD studies have now become an essential weapon in the designer's armoury, the other two still rely mostly on experimental research. Possible further developments are discussed.