During operation with so-called advanced scenarios in a tokamak, current holes, characterized by a virtually current-free central region, often develop. They might also be difficult to avoid, at least transiently, in reactor plasmas. This paper is focused on how the presence of a current hole affects quantities related to fusion born alpha particles. In particular, the anisotropy in the fast ion pressure, the current they generate and the profile of the power they transfer to the thermal plasma via collisions. Possible implications for the confinement of the alpha particles and the performance of the plasma are discussed. Furthermore, the results of a comparison between simulations and gamma-ray data from recent JET trace tritium experiments with current holes are presented.