This report presents findings from a literature review and survey undertaken as part of the SHAPE-ID Horizon 2020 project (https://www.shapeid.eu), which addresses the challenge of improving interdisciplinary research (IDR) and transdisciplinary research (TDR) between Arts, Humanities and Social Sciences (AHSS) and Science, Technology, Engineering, Mathematics, and Medicine (STEMM) disciplines. One of SHAPE-ID’s first objectives was to review existing research on IDR/TDR. Through an extensive evidence-scanning exercise drawing on previous work undertaken and complemented by a survey and interviews, the project aimed: (i) to disentangle the different understandings of interdisciplinarity and transdisciplinarity; (ii) to identify the factors that hinder or help inter- and transdisciplinary collaboration; (iii) to clarify which understandings of IDR/TDR and which factors of success and failure are specifically relevant for integrating AHSS in IDR/TDR.