Ionic liquids (ILs) have attracted great attention as green solvents, heat carriers, and electrolytes. They can be obtained with specific thermophysical properties and functions by changing the kind of species of cations and anions. Knowledge of the fundamental thermophysical properties of ILs, such as their densities, viscosities, and thermal conductivities, is needed to design ILs with desirable thermophysical properties. In this chapter, we will review the various measurement results for the thermal conductivities of the pure components of ILs and methods for predicting the thermal conductivity of an IL, which are based on its structure and physical properties, by conducting correlations between these parameters. In the recent years, the thermal conductivities of IoNano fluids, which comprise of nanoparticles dispersed in an IL, have attracted great attention. Therefore, we will review the unique thermal conductivities of IoNano fluids.