Recent artificial-grammar learning (AGL) paradigms driven by the Chomsky hierarchy paved the way for direct comparisons between humans and animals in the learning of center embedding ([A[AB]B]). The AnBn grammars used by the first generation of such research lacked a crucial property of center embedding, where the pairs of elements are explicitly matched ([A1 [A2 B2] A1]). This type of indexing is implemented in the second-generation AnBn grammars. This paper reviews recent studies using such grammars. Against the premises of these studies, we argue that even those newer AnBn grammars cannot test the learning of syntactic hierarchy. These studies nonetheless provide detailed information about the conditions under which human adults can learn an AnBn grammar with indexing. This knowledge serves to interpret recent animal studies, which make surprising claims about animals’ ability to handle center embedding.