Can nonhuman animals perceive the relation-between-relations? This intriguing question has been studied over the last 40 years; nonetheless, the extent to which nonhuman species can do so remains controversial. Here, I review empirical evidence suggesting that pigeons, parrots, crows, and baboons join humans in reliably acquiring and transferring relational matching-to-sample (RMTS). Many theorists consider that RMTS captures the essence of analogy, because basic to analogy is appreciating the ‘relation between relations.’ Factors affecting RMTS performance include: prior training experience, the entropy of the sample stimulus, and whether the items that serve as sample stimuli can also serve as choice stimuli.