We outline the Berlin Brain-Computer Interface (BBCI), a system which enables us to translate brain signals from movements or movement intentions into control commands. The main contribution of the BBCI, which is a non-invasive EEG-based BCI system, is the use of advanced machine learning techniques that allow to adapt to the specific brain signatures of each user with literally no training. In BBCI a calibration session of about 20min is necessary to provide a data basis from which the individualized brain signatures are inferred. This is very much in contrast to conventional BCI approaches that rely on operand conditioning and need extensive subject training of the order 50-100 hours. Our machine learning concept thus allows to achieve high quality feedback already after the very first session. This work reviews a broad range of investigations and experiments that have been performed within the BBCI project. In addition to these general paradigmatic BCI results, this work provides a ...