Affective states, moods and emotions, are an integral part of human nature: they shape our thoughts, govern the behavior of the individual, and influence our interpersonal relationships. The last decades have seen a growing interest in the automatic detection of such states from voice, facial expression, and physiological signals, primarily with the goal of enhancing human-computer interaction with an affective component. With the advent of brain-computer interface research, the idea of affective brain-computer interfaces (aBCI), enabling affect detection from brain signals, arose. In this article, we set out to survey the field of neurophysiology-based affect detection. We outline possible applications of aBCI in a general taxonomy of brain-computer interface approaches and introduce the core concepts of affect and their neurophysiological fundamentals. We show that there is a growing body of literature that evidences the capabilities, but also the limitations and challenges of affect detection from neurophysiological activity.