Sequential learning plays a role in a variety of common tasks, such as human language processing, animal communication, and the learning of action sequences. In this article, we investigate sequential learning in non-human primates from a comparative perspective, focusing on three areas: the learning of arbitrary, fixed sequences; statistical learning; and the learning of hierarchical structure. Although primates exhibit many similarities to humans in their performance on sequence learning tasks, there are also important differences. Crucially, non-human primates appear to be limited in their ability to learn and represent the hierarchical structure of sequences. We consider the evolutionary implications of these differences and suggest that limitations in sequential learning may help explain why non-human primates lack human-like language.