We have developed empirical interatomic potentials for studying radiation defects and dislocations in tungsten. The potentials use the embedded atom method formalism and are fitted to a mixed database, containing various experimentally measured properties of tungsten and ab initio formation energies of defects, as well as ab initio interatomic forces computed for random liquid configurations. The availability of data on atomic force fields proves critical for the development of the new potentials. Several point and extended defect configurations were used to test the transferability of the potentials. The trends predicted for the Peierls barrier of the 1/2 {111} screw dislocation are in qualitative agreement with ab initio calculations, enabling quantitative comparison of the predicted kink-pair formation energies with experimental data.