Music is a fascinating and complex aspect of cognition. When listening to music, listeners may experience complex structural relations, many of which are characterized in great detail by music-theoretical accounts. Such cognitive experience of structure in music, however, presents many challenges for empirical investigation: structural interpretations are the result of an inference on the part of the listener, resulting in ambiguous interpretations that listeners cannot often report explicitly. As a comparison, language comprehenders are also sensitive to the syntactic structure of sentences, and psycholinguistic research has an extensive track-record in investigating what representations of syntactic structure look like, and how they are formed in real-time processing. Could we achieve a similar understanding for music too? The goal of the symposium is to reflect on the challenges and prospects of such an endeavour: What can we learn from behavioural and brain-imaging experiments about the cognitive reality of musical structures? How do empirical observations pertaining to prediction and processing complexity relate to theoretical frameworks of musical structure?