Neuroaesthetics is a young field of research concerned primarily with the neural basis of cognitive and affective processes engaged when an individual takes an aesthetic or artistic approach towards a work of art, a non-artistic object or a natural phenomenon. In September 2009, the "Copenhagen Neuroaesthetics Conference" brought together leading researchers in the field to present and discuss current advances. We summarize some of the principal themes of the conference, placing neuroaesthetics in a historical context and discussing its scope and relation to other disciplines. We also identify what we believe to be the key outstanding questions, the main pitfalls and challenges faced by the field, and some promising avenues for future research.