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Analogical reasoning is a core facet of higher cognition in humans. Creating analogies as we navigate the environment helps us learn. Analogies involve reframing novel encounters using knowledge of familiar, relationally similar contexts stored in memory. When an analogy links a novel encounter with a familiar context, it can aid in problem solving. Reasoning by analogy is a complex process that is mediated by multiple brain regions and mechanisms. Several advanced computational architectures have been developed to simulate how these brain processes give rise to analogical reasoning, like the "learning with inferences and schema abstraction" architecture and the Companion architecture. To obtain this power to simulate human reasoning, theses architectures assume that various computational "subprocesses" comprise analogical reasoning, such as analogical "access," "mapping," "inference," and "schema induction," consistent with the structure-mapping framework proposed decades ago. However, little is known about how these subprocesses relate to actual brain processes. While some work in neuroscience has linked analogical reasoning to regions of brain prefrontal cortex, more research is needed to investigate the wide array of specific neural hypotheses generated by the computational architectures. In the current article, we review the association between historically important computational architectures of analogy and empirical studies in neuroscience. In particular, we focus on evidence for a frontoparietal brain network underlying analogical reasoning and the degree to which brain mechanisms mirror the computational subprocesses. We also offer a general vantage on the current- and future-states of neuroscience research in this domain and provide some recommendations for future neuroimaging studies.