The vermiform appendix is the primary site of several distinctive benign and malignant neoplasms. Some can produce the clinical syndrome of pseudomyxoma peritonei (PMP). A consensus on their terminology was reached by an international panel of pathologists and clinicians working under the auspices of the Peritoneal Surface Oncology Group International (PSOGI), and this review discusses the application of the PSOGI classification to routine reporting. We discuss diagnosis and differential diagnosis together with implications for patient management, covering low‐grade appendiceal mucinous neoplasms, high‐grade appendiceal mucinous neoplasms, serrated polyps, adenomas and adenocarcinomas. We do not cover goblet cell tumours or neuroendocrine neoplasms in this paper.