We first review analytical and computer modelling approaches to heat conduction in insulating liquids. Thermal conductivity Δ can be calculated by approximate analytic theory, and also by molecular simulation which solves the many-body problem for molecules interacting through specific interactions. Equilibrium and non-equilibrium molecular dynamics, NEMD, techniques are now available that enable Δ to be computed for single-component monatomic and molecular liquids, as well as their mixtures. For mixtures, Δ can be determined from the distinct Onsager coefficients, individually computed using equilibrium molecular dynamics. Electronic contributions to the thermal conductivity of liquid metals are then considered, by invoking the Wiedemann-Franz Law relating thermal and electrical transport.