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 condensed outline of the underlying machine learning and signal processing techniques that make the BBCI succeed. In the first experimental paradgm we analyze the predictability of limb movement long before the actual movement takes place using only the movement intention measured from the pre-movement (readiness) EEG potentials. The experiments include both off-line studies and an online feedback paradigm. The limits with respect to the spatial resolution of the somatotopy are explored by contrasting brain patterns of movements of left vs. right hand rsp. foot. In a second conplementary paradigm voluntary modulations of sensorimotor rhythms caused by motor imagery (left hand vs. right hand vs. foot) are translated into a continuous feedback signal. Here we report results of a recent feedback study with 6 healthy subjects with no or very little experience with BCI control: half of the subjects achieved an information transfer rate above 35 bits per minute (bmp). Furthermore one subject used the BBCI to operate a mental typewriter in free spelling mode. The overall spelling speed was 4.5-8 letters per minute including the time needed for the correction errors.