This paper outlines three important challenges to the idea that there can be such a thing as non-sensible or intelligible beauty: (i) the perceptual challenge, (ii) the conflation challenge and (iii) the reductivism challenge. Whilst not conclusive, these challenges bring out aspects of the intelligibility ascribed to some instances of beauty which stand in need of further clarification if a credible theory of intelligible beauty is to be defended. A critical discussion of each challenge leads us to consider a conception of the notion of intelligible beauty that is not entirely disassociated from perceptual sense-experience or peripheral to aesthetic value in general. 

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