Thermophysical properties of engineering fluids have proven in the past to be essential for the design of physical and chemical processing and reaction equipment in the chemical, metallurgical, and allied industries, as they influence directly the design parameters and performance of plant units in the of, for example, heat exchangers, distillation columns, phase separation, and reactors. In the energy field, the search for the optimization of existing and alternative fuels, either using neutral or ionic fluids, is an actual research and application topic, both for new applications and the sustainable development of old technologies. One of the most important drawbacks in the industrial use of thermophysical property data is the common discrepancies in available data, measured with different methods, different samples, and questionable quality assessment. Measuring accurately the thermal conductivity of fluids has been a very successful task since the late 1970s due to the efforts of several schools in Europe, Japan, and the United States. However, the application of the most accurate techniques to several systems with technological importance, like ionic liquids, nanofluids, and molten salts, has not been made in the last ten years in a correct fashion, generating highly inaccurate data, which do not reflect the real physical situation. It is the purpose of this paper to review critically the best available techniques for the measurement of thermal conductivity of fluids, with special emphasis on transient methods and their application to ionic liquids, nanofluids, and molten salts.