We first review analytical and computer modelling approaches to heat c
onduction in insulating liquids. Thermal conductivity lambda can be ca
lculated by approximate analytic theory, and also by molecular simulat
ion which solves the many-body problem for molecules interacting throu
gh specific interactions. Equilibrium and non-equilibrium molecular dy
namics, NEMD, techniques are now available that enable lambda to be co
mputed for single-component monatomic and molecular liquids, as well a
s their mixtures. For mixtures, lambda can be determined from the dist
inct Onsager coefficients, individually computed using equilibrium mol
ecular dynamics: Electronic contributions to the thermal conductivity
of liquid metals are then considered, by invoking the Wiedemann-Franz
Law relating thermal and electrical transport.