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High temperature heat transfer fluids like molten salts and molten metals will unlock the higher efficiency and lower cost of next generation grid scale energy sources such as concentrated solar power and advanced nuclear power plants. Their thermal conductivity will help determine how much heat power can be extracted from high temperature systems to do useful work. However, there is a large spread in liquid thermal conductivity data at high temperatures, and well-established, general models of liquid thermal conductivity across liquid classes and temperature ranges are lacking. In this work, we review experimental techniques used to measure liquid thermal conductivity – various steady-state, time-domain, and frequency-domain techniques – and we discuss strategies to minimize errors from convection, radiation, and corrosion that are amplified at high temperature. We classify liquids based on their dominant intermolecular interaction (simple, molecular, coulombic, or metallic) and examine their resulting short-range order that will inform models of heat conduction in liquids. Through the lens of intermolecular interactions and short-range order in liquids, we review previous analytical models of liquid thermal conductivity – modified kinetic gas, quasi-crystalline, and electron dominated models – and we compare their results with reliable experimental measurements of various types of liquids. The results suggest that modified kinetic gas models do not match experimental data for liquids. Quasi-crystalline models can accurately match some available experimental results of molten salts. We explore underlying similarities between various quasi-crystalline models that may be explained by frequency dependent vibrational modes in liquids. Electron transport is the dominant mechanism for thermal conductivity in molten metals. However electrical conductivity measurements cannot be used directly for molten metal thermal conductivity measurement using the Wiedemann-Franz law because the Lorentz number varies with pressure, temperature and metal composition. In addition to analytical models we review molecular dynamics simulations, using equilibrium and non-equilibrium methods. The results show that MD simulations for molten salt thermal conductivity slightly overpredict experimentally measured reference values. These simulations can provide insights into the frequency-dependent behavior of vibrational modes in liquids. Lastly, we discuss future research directions of high temperature liquid thermal conductivity research and provide an outlook for applications for high temperature heat transfer fluids including use in power generation. [ABSTRACT FROM AUTHOR]