We asked whether and how people appreciate ambiguous artworks and examined the possible mechanisms underlying the appeal of perceptual challenge in art. Although experimental research has shown people’s particular appreciation for highly familiar and prototypical objects that are fluently processed, there is increasing evidence that in the arts people often prefer ambiguous materials which are processed less fluently. Here, we empirically show that modern and contemporary ambiguous artworks evoking perceptual challenge are indeed appreciated. By applying a multilevel modeling approach together with multidimensional measurement of aesthetic appreciation, we revealed that the higher the subjectively perceived degree of ambiguity within an artwork, the more participants liked it and the more interesting and affecting it was for them. These dimensions of aesthetic appreciation were also positively related to the subjectively reported strength of insights during elaboration of the artworks. The estimated solvability of the experienced ambiguity, in contrast, was not relevant for liking and even negatively linked to interest and affect. Consequently, we propose a critical view of the frequently reported idea that processing (modern) art simply equals a kind of problem solving task. We suggest the dynamic gain of insights during the elaboration of an ambiguous artwork, rather than the state of having solved a problem, to be a mechanism possibly relevant to the appeal of challenge in the perception of ambiguous art.