People with severe neurological impairments face many challenges in sensorimotor functions and communication with the environment; therefore they have increased demand for advanced, adaptive and personalized rehabilitation. During the last several decades, numerous studies have developed brain-computer interfaces (BCIs) with the goals ranging from providing means of communication to functional rehabilitation. Here we review the research on non-invasive, electroencephalography (EEG)-based BCI systems for communication and rehabilitation. We focus on the approaches intended to help severely paralyzed and locked-in patients regain communication using three different BCI modalities: slow cortical potentials, sensorimotor rhythms and P300 potentials, as operational mechanisms. We also review BCI systems for restoration of motor function in patients with spinal cord injury and chronic stroke. We discuss the advantages and limitations of these approaches and the challenges that need to be addressed in the future.