The coupling between a ferromagnet and an antiferromagnet can give rise to a directional anisotropy called exchange bias. In order to establish the direction of the exchange bias, the coupled ferro-/antiferromagnetic system is generally cooled in the presence of an external magnetic field through the ordering temperature of the antiferromagnet. In many systems the magnitude of the exchange bias is reduced upon subsequent field cycling after the initial field cooling. These field-training effects are suspected to be due to irreversible changes in the magnetic microstructure of the antiferromagnet, but a comprehensive theoretical understanding is still missing. I will present numerical simulations based on a simple coherent rotation model, which suggest that the symmetry of the anisotropy in the antiferromagnet plays a crucial role for the understanding of these training effects. Namely, the existence of more than one antiferromagnetic easy anisotropy axes can initially stabilize a non-collinear arrangement of the antiferromagnetic spins, which relaxes into a collinear arrangement after the first magnetization reversal of the ferromagnet. This explains quite naturally why training effects are only observed for exchange bias systems with high symmetry antiferromagnets, while they are absent for antiferromagnets with uniaxial anisotropy. Furthermore, this simple and universal model reproduces many of the experimentally observed training effects. The model gives rise to a rotation of the effective easy axis for the ferromagnet after the first field reversal, such that the first magnetization reversal shows a large sudden jump, while all subsequent reversals are more gradual. I will compare in detail the calculated hysteresis loops with experimentally measured ones on the prototypical Co/CoO exchange bias system. This work was supported by the Department of Energy, Basic Energy Sciences under contract No. W-31-109-ENG-38.