Each of our senses is 'blind' to some features of objects and events (e.g., hearing can tell us little or nothing about the shape, colour, and weight of an object, or about how it might taste or smell). When we listen to sounds without support from other sensory modalities, such as when listening to recorded music, how do will fill-in these blind spots? Evidence identifying a core set of cross-sensory correspondences among basic stimulus features is reviewed, and it is proposed that they offer a potential basis for the filling-in of information that is missing when one or more sensory systems is not available. An emerging theoretical framework for understanding correspondences and their impact on behaviour is presented. Evidence pertaining to key features of the framework is reviewed, including that cross-sensory correspondences are based on cross-talk among conceptual representations of aligned feature dimensions, are bi-directional in their effects, obey transitivity in the feature associations they support, involve the relative (context-sensitive) coding of stimulus features, and can be accessed through the verbal specification of feature values. After illustrating how cross-sensory correspondences are able to embrace basic features of bodily actions, gestures, and vocalisations, their potential for exploitation in the communication of ideas is explained. The relevance of cross-sensory correspondences to musical sounds, and their potential to enhance the composition, performance, and appreciation of music, are discussed.