Tumours of the appendix - a vestigial digestive organ attached to the colon - are rare. Although we estimate that around 3,000 new appendiceal cancer cases are diagnosed annually in the USA, the challenges of accurately diagnosing and identifying this tumour type suggest that this number may underestimate true population incidence. In the current absence of disease-specific screening and diagnostic imaging modalities, or well-established risk factors, the incidental discovery of appendix tumours is often prompted by acute presentations mimicking appendicitis or when the tumour has already spread into the abdominal cavity - wherein the potential misclassification of appendiceal tumours as malignancies of the colon and ovaries also increases. Notwithstanding these diagnostic difficulties, our understanding of appendix carcinogenesis has advanced in recent years. However, there persist considerable challenges to accelerating the pace of research discoveries towards the path to improved treatments and cures for patients with this group of orphan malignancies. The premise of this Expert Recommendation article is to discuss the current state of the field, to delineate unique challenges for the study of appendiceal tumours, and to propose key priority research areas that will deliver a more complete picture of appendix carcinogenesis and metastasis. The Appendix Cancer Pseudomyxoma Peritonei (ACPMP) Research Foundation Scientific Think Tank delivered a consensus of core research priorities for appendiceal tumours that are poised to be ground-breaking and transformative for scientific discovery and innovation. On the basis of these six research areas, here, we define the first 'cells to society' research framework for appendix tumours.