The wall temperatures at curved leading edges of blades and vanes in gas turbines have to be maintained below the melting point, e.g. by applying impingement cooling. Hence, impingement cooling of concave surfaces directly contributes to an elevated turbine inlet temperature guaranteeing safe operation, elongated life cycles and high thermal efficiency at the same time. This thesis aims to investigate impingement cooling on the concave leading edge of a generic gas turbine blade geometry with sophisticated experimental and numerical methods. The transient Thermochromic Liquid Crystal (TLC) technique is applied at the test rig to determine spatially resolved heat transfer coefficients. The steady state 3D Computational Fluid Dynamics (CFD) simulations are conducted in OpenFOAM and utilize the Shear-Stress-Transport (SST) turbulence model. A variety of geometric and operational parameters like the separation distance, the crossflow configuration and the Reynolds number are studied to determine their impact on the overall heat transfer performance. First, the smooth concave leading edge is analyzed. The agreement between CFD simulations and is good with a maximum deviation of 8.3% for the global Nusselt number. In general, larger Reynolds numbers and smaller separation distances increase the heat transfer level, while the presence of crossflow lowers the local Nusselt numbers and yields a more homogeneous heat transfer distribution. Second, a rib roughened target surface is investigated to maximize the heat transfer performance of the impingement cooling array. A regular V-rib shape is chosen and projected onto the concave target yielding curved rib edges. In the wake of the ribs, a significant Nusselt number increase compared to the smooth case is evident in the experimental and CFD simulation data, which agree well. The dependency of the heat transfer performance on the number of ribs, the rib position and the Reynolds number is investigated.