[en] Fast, supra-thermal ions provide a powerful mechanism to heat fusion plasmas. Through Coulomb collisions with the thermal bulk plasma, they slow down and transfer their energy to the plasma. In present-day devices, fast ions are generated by neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH). In future fusion reactors, the dominant heating source, which allows the ignition of a burning plasma, will be fast a-particles resulting from fusion reactions. In addition to plasma heating, fast ions can be utilized to drive plasma currents and rotation. It is therefore crucial for the success of future fusion devices (such as ITER and DEMO) to understand the physics of fast ions and ensure their safe confinement. This thesis focuses both on modeling and experimental aspects. A model to calculate the NBI fast-ion distribution rapidly has been developed. It is based on a combination of existing codes and analytic solutions. Due to the comparably low numerical effort, it can be used to calculate the fast-ion distribution in a large set of discharges, which is used to e.g. improve plasma equilibrium reconstructions. Experimentally, the physics of fast ions is investigated at the tokamak ASDEX Upgrade, using a FIDA (Fast-Ion D-Alpha) spectroscopy diagnostic. This diagnostic technique is based on charge-exchange reactions, that convert the ions into neutral atoms (keeping their momenta). The light emission from these neutral atoms can be collected by optics in the machine and analyzed with spectrometers. Here, the fast-ion contribution can be identified due to large Doppler shifts, and the shape of the spectrum yields information about the velocity distribution. The Doppler shift is given by a projection of the ion velocity vector onto the line of sight, such that observation from different viewing angles is needed to cover the entire velocity space. Therefore, the FIDA diagnostic has been upgraded from three viewing arrays to five, and the spectrometer has been redesigned to measure blue and red Doppler shifts simultaneously. These upgrades allow a tomographic reconstruction of the 2D fast-ion velocity distribution at several well-defined measurement positions. The tomography has been successfully tested analyzing different fast-ion populations in plasmas free of instabilities. These enhanced diagnostic capabilities are used to study fast-ion transport caused by plasma instabilities. In particular, the velocity-space dependence of the fast-ion redistribution during sawtooth crashes is investigated. It is found, that fast ions with high velocity components perpendicular to the magnetic field are less affected by sawtooth crashes than other fast ions, and theoretical explanations for these observations are discussed. In addition, radial redistribution by Alfven eigenmodes is analyzed. Significant radial fast-ion redistribution is found in the presence of a reversed-shear Alfven eigenmode cascade. Furthermore, the acceleration of fast deuterium beam ions by 2nd harmonic ion cyclotron heating is investigated. This is important, because future fusion devices are foreseen to use 2nd harmonic absorption as heating scheme, in contrast to 1st harmonic minority ICRH, which is used in most present-day devices. Hence, the physic principles of 2nd harmonic absorption must be investigated and well understood in order to ensure, that theoretical predictions for e.g. ITER are correct. In the tomographic reconstruction of FIDA signals, clear high energy tails due to 2nd harmonic ICRH are seen, and comparisons to theoretical codes are presented.