Much like most of cognition research, music cognition is an interdisciplinary field, which attempts to apply methods of cognitive science (neurological, computational and experimental) to understand the perception and process of composition of music. In this paper, we first motivate why music is relevant to cognitive scientists and give an overview of the approaches to computational modelling of music cognition. We then review literature on the various models of music perception, including non-computational models, computational non-cognitive models and computational cognitive models. Lastly, we review literature on modelling the creative behaviour and on computer systems capable of composing music. Since a lot of technical terms from music theory have been used, we have appended a list of relevant terms and their definitions at the end.