Radiation therapy is one of the cornerstones of modern cancer treatment, and at the Heidelberg Ion Beam Therapy Centre, tumors are treated with protons, helium ions and carbon ions. For this, the precise delivery of thousands of individual beamlets is necessary. Planning such complex treatments is unthinkable without dose calculation algorithms, and in terms of accuracy, Monte Carlo (MC) algorithms like FLUKA are seen as the gold standard. However, due to their long runtimes, they are limited to nonurgent applications. To meet the demand of clinicians and researchers for fast dose estimation, the focus in recent years has been on the development of fast MC algorithms that combine speed and accuracy. While many fast proton MC codes exist, there is a lack of fast MC algorithms capable of supporting the full range of ions used at HIT. The aim of this thesis, which is a cumulative work consisting of three publications, is to provide an overview of the development and validation of MonteRay, a fast and precise MC dose calculation engine for protons, helium ions, and carbon ions. In the accompanying publications, MonteRay is compared against a wide range of measurements and other dose engines, achieving excellent results in terms of accuracy while being significantly faster than FLUKA, with speedups between approximately 15 and 70, depending on the energy and ion type.