Brain-computer interfaces (BCIs) promise to provide a novel access channel for assistive technologies, including augmentative and alternative communication (AAC) systems, to people with severe speech and physical impairments (SSPI). Research on the subject has been accelerating significantly in the last decade and the research community took great strides toward making BCI-AAC a practical reality to individuals with SSPI. Nevertheless, the end goal has still not been reached and there is much work to be done to produce real-world-worthy systems that can be comfortably, conveniently, and reliably used by individuals with SSPI with help from their families and care givers who will need to maintain, setup, and debug the systems at home. This paper reviews reports in the BCI field that aim at AAC as the application domain with a consideration on both technical and clinical aspects.