In this paper, the importance of the challenge associated with the control of the thermal conductivity of thermal barrier coatings for aircraft turbine hot stages is reviewed. It is firstly illustrated by the description of a practical aeronautic coated and uncoated turbine blade design exercise. The various contributions to TBC thermal conductivity are then exposed. Their low conductivity finds its source not only in the nature of the ceramic layer, but also in the morphology of the insulating layer, closely linked to its fabrication process parameters. The influence of various factors (such as yttria content, temperature, porosity content and distribution, etc.) on the thermal conductivity is examined, largely based on a literature review. In this field of investigation, the modelling tool should allow to predict, to a certain extent, which morphology would lead to the lowest values of thermal conductivity. Eventually, attempts are made to identify research domains where further understanding is needed, and to formulate several suggestions concerning possible ways to lower the thermal conductivity.