Although the field of Brain-Computer Interfacing (BCI) has made incredible advances in the last decade, current BCIs are still scarcely used outside laboratories. One reason is the lack of robustness to noise, artifacts and nonstationarity which are intrinsic parts of the recorded brain signal. Furthermore out-of-lab environments imply the presence of external variables that are largely beyond the control of the user, but can severely corrupt signal quality. This paper presents a new generation of robust EEG signal processing approaches based on the information geometric notion of divergence. We show that these divergence-based methods can be used for robust spatial filtering and thus increase the systems' reliability when confronted to, e.g., environmental noise, users' motions or electrode artifacts. Furthermore we extend the divergence-based framework to heavy-tail distributions and investigate the advantages of a joint optimization for robustness and stationarity.