Measurements of the thermal conductivity (kxx) and the thermal Hall effect (kxy) in high magnetic fields in Y-and Bi-based high-Tc superconductors are presented. We describe the experimental technique and test measurements on a simple metal (niobium). In the high-Tc superconductors kxx and kxy increase below Tc and show a maximum in their temperature dependence. kxx has contributions from phonons and quasiparticle (QP) excitations, whereas kxy is purely electronic. The strong increase of kxy below Tc gives direct evidence for a strong enhancement of the QP contribution to the heat current and thus for a strong increase of the QP mean free path. Using kxy and the magnetic field dependence of kxx we separate the electronic thermal conductivity (k el xx ) of the CuO2-planes from the phononic thermal conductivity (k ph xx ). In YBa2Cu3O 7−δ k el xx shows a pronounced maximum in the superconducting state. This maximum is much weaker in Bi2Sr2CaCu2O 8+δ , due to stronger impurity scattering. The maximum of k el xx is strongly suppressed by a magnetic field, which we attribute to the scattering of QPs on vortices. An additional magnetic field independent contribution to the maximum of kxx occurs in YBa2Cu3O 7−δ , reminiscent of the contribution of the CuO-chains, as determined from the anisotropy in untwined single crystals. Our data analysis reveals that below Tc as in the normal state a transport (τ ) and a Hall (τH) relaxation time must be distinguished: The inelastic (i.e. temperature dependent) contribution to τ is strongly enhanced in the superconducting state, whereas τH displays the same temperature dependence as above Tc. We determine also the electronic thermal conductivity in the normal state from kxy and the electrical Hall angle. It shows an unusual linear increase with temperature.