Pseudomyxoma Peritonei (PMP) is a rare peritoneal malignancy, most commonly originating from a perforated epithelial tumour of the appendix. Given its rarity, randomized controlled trials on treatment strategies are lacking, nor likely to be performed in the foreseeable future. However, many questions regarding the management of appendiceal tumours, especially when accompanied by PMP, remain unanswered. This consensus statement was initiated by members of the Peritoneal Surface Oncology Group International (PSOGI) Executive Committee as part of a global advisory role in the management of uncommon peritoneal malignancies. The manuscript concerns an overview and analysis of the literature on mucinous appendiceal tumours with, or without, PMP. Recommendations are provided based on three Delphi voting rounds with GRADE-based questions amongst a panel of 80 worldwide PMP experts.