The core of terrestrial planets, including Earth, Mars, and Mercury, etc., is majorly composed of iron alloyed with some lighter elements, such as silicon, sulfur, carbon, oxygen, and hydrogen. Core's thermal conductivity plays a key role in controlling its cooling rate, dynamics, thermochemical and dynamo evolution, as well as available energy budget to power dynamo for magnetic field. Recent successful advances in coupling an ultrafast optical pump-probe method with externally-and laser-heated diamond anvil cells have enabled us to precisely and systematically measure the thermal conductivity of a number of candidate core materials in terrestrial planets. With data modelling, we have created the first version of thermal conductivity profiles in the deep interiors of Earth and Mars, with potential critical impacts on their core's thermochemical and dynamo evolution. We acknowledge funding support from the Academia Sinica and the National Science and Technology Council of Taiwan, Republic of China, under Contract AS-IA-111-M02 and 113-2628-M-001-013-. The works presented here are also co-authored with Jung