Extracting the regularities of our environment is a core cognitive ability in human and non‐human primates. Comparative studies may provide information of strong heuristic value to constrain the elaboration of computational models of regularity learning. This study illustrates this point by testing human and non‐human primates (Guinea baboons, Papio papio) with the same experimental paradigm, using a novel online learning measure. For local co‐occurrence regularities, we found similar patterns of regularity extraction in baboons and humans. However, only humans extracted the more global sequence structure. It is proposed that only the first result that is common to both species should be used to constrain models of regularity learning. The second result indicates that the extraction of global regularities cannot be accounted for by mere associative learning mechanisms and suggests that humans probably benefit from their language recoding abilities for extracting these regularities. We propose to use a comparative approach to address a series of remaining theoretical questions, which will contribute to the development of a general theory of regularity learning.