Background: Knowledge about the brain has been growing rapidly since the 1990s as a result of developments in neuroscientific research linked to improvements in functional neuroimaging and other brain imaging technologies. As the brain is the "principal organ involved in learning" (1), it would seem reasonable to assume that education should be one of the chief beneficiaries of this research, leading to advances in our understanding of how people learn, the development of new curricula and innovative teaching and learning approaches. However, the linkage between neuroscience and education has, historically, always been weak, and, we suggest, continues to be so, notwithstanding important research initiatives since the year 2000. Purpose: The purpose of this paper is to critically explore current theoretical understanding of joint neuroscientific and educational research, herein referred to as "neuroeducational" research. There is a particular focus on a critique of the transdisciplinary model as applied in a study of imitation in learners with autism. Main argument and sources of evidence: The review of the literature in the first half of the paper identifies the key barriers to neuroeducational research, including neuromyths, lack of shared understanding, the problem of the translation of neuroscientific findings to schools and clashing research assumptions, methodologies and traditions. However, a model of transdisciplinarity is presented as a possible way forward. This model is tested in the second half of the paper against the experiences of the authors in conducting transdisciplinary research in autism and imitation in the secondary classroom. Here, we develop the concepts of "transfer affordances", "transfer challenges" and "transfer opportunities" to structure our analysis of the various dimensions of the transdisciplinary research process. These new concepts are defined, and their relevance and utility explained. Conclusions: The main conclusion of the paper is that the transdisciplinary research process within neuroeducation is complex, far from fully understood and requires further mapping. It is proposed that the concepts of "transfer affordances", "transfer challenges" and "transfer opportunities" are useful theoretical ideas in pursuit of this aim.