The rapid growth of cultural evolutionary science, its expansion into numerous fields, its use of diverse methods, and several conceptual problems have outpaced corollary developments in theory and philosophy of science. This has led to concern, exemplified in results from a recent survey conducted with members of the Cultural Evolution Society, that the field lacks ‘knowledge synthesis’, is poorly supported by ‘theory’, has an ambiguous relation to biological evolution and uses key terms (e.g. ‘culture’, ‘social learning’, ‘cumulative culture’) in ways that hamper operationalization in models, experiments and field studies. Although numerous review papers in the field represent and categorize its empirical findings, the field's theoretical challenges receive less critical attention even though challenges of a theoretical or conceptual nature underlie most of the problems identified by Cultural Evolution Society members. Guided by the heterogeneous ‘grand challenges’ emergent in this survey, this paper restates those challenges and adopts an organizational style requisite to discussion of them. The paper's goal is to contribute to increasing conceptual clarity and theoretical discernment around the most pressing challenges facing the field of cultural evolutionary science. It will be of most interest to cultural evolutionary scientists, theoreticians, philosophers of science and interdisciplinary researchers.