This paper summarizes the state-of-the-art related to the heat transfer characteristics of narrow impingement cooling channels, which can nowadays be integrated within the external wall of turbine airfoils. Particular emphasis is given to the experimental outcomes of the research activities performed at the Group of Thermal Turbomachinery (GTT) of EPFL over the last 10 years. The influence of various geometrical factors on the heat transfer distributions is demonstrated, aiming to provide a summarized physical knowledge for the thermal design of such configurations. More specifically, effects of channel height and width, streamwise jet-to-jet spacing, impingement hole staggering arrangements, varying jet diameters, convergent and divergent channel geometries, as well as effects of number of holes, are addressed for all channel interior surfaces. Existing correlations are also presented and compared to empirical models derived from traditional multi-array impingement jet systems. Furthermore, future research directions in the form of sequential impingement cascades are also discussed.