The past two decades have seen an explosion of research on cross-modal correspondences. Broadly speaking, this term has been used to encompass associations between and among features, dimensions, or attributes across the senses. There has been an increasing interest in this topic amongst researchers from multiple fields (psychology, neuroscience, music, art, environmental design, etc.) and, importantly, an increasing breadth of the topic's scope. Here, this narrative review aims to reflect on what cross-modal correspondences are, where they come from, and what underlies them. We suggest that cross-modal correspondences are usefully conceived as relative associations between different actual or imagined sensory stimuli, many of these correspondences being shared by most people. A taxonomy of correspondences with four major kinds of associations (physiological, semantic, statistical, and affective) characterizes cross-modal correspondences. Sensory dimensions (quantity/quality) and sensory features (lower perceptual/higher cognitive) correspond in cross-modal correspondences. Cross-modal correspondences may be understood (or measured) from two complementary perspectives: the phenomenal view (perceptual experiences of subjective matching) and the behavioural response view (observable patterns of behavioural response to multiple sensory stimuli). Importantly, we reflect on remaining questions and standing issues that need to be addressed in order to develop an explanatory framework for cross-modal correspondences. Future research needs (a) to understand better when (and why) phenomenal and behavioural measures are coincidental and when they are not, and, ideally, (b) to determine whether different kinds of cross-modal correspondence (quantity/quality, lower perceptual/higher cognitive) rely on the same or different mechanisms.