The increased biological effectiveness of heavy charged particle beams like e.g., carbon ions in the tumor volume in comparison to the lower effectiveness in the surrounding healthy tissue represents one of the major rationales for their application in tumor therapy. This increased effectiveness also characterizes the advantage of heavier ions compared to proton beams. The increased effectiveness has to be taken into account in treatment planning in order to estimate the corresponding photon equivalent doses in normal and tumor tissues, thus allowing a link e.g., to normal tissue dose limits in conventional photon therapy. Due to the complex dependencies of RBE on parameters like dose, beam energy, LET, atomic number and cell or tissue type, the relevant RBEs cannot be solely determined from experimental data. Therefore, within the framework of the pilot project of tumor therapy with carbon ions performed at GSI Darmstadt, treatment planning is based on a biophysical model, which has been extensively tested. The paper first summarizes the essential systematic dependencies of RBE on different parameters like e.g., dose, LET, atomic number and cell type. The basic principle of the biophysical model is then introduced, and special emphasis is given to the application of the model to in vivo and clinical endpoints. Model predictions are compared to experimental data in vitro and in vivo. Finally, the implementation of the biophysical model in the treatment planning procedure is presented. The biological verification of the whole treatment planning procedure is explained and examples of patient treatment plans are given.