We first review analytical and computer modelling approaches to heat conduction in insulating liquids. Thermal conductivity lambda 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 lambda to be computed for single-component monatomic and molecular liquids, as well as their mixtures. For mixtures, lambda 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.