Low grade appendiceal mucinous neoplasms can spread to the peritoneum as pseudomyxoma peritonei even though they are not obviously invasive in the appendix. During the past several decades, several problematic issues surrounding this enigmatic tumor have been debated in the literature, including appropriate nomenclature for the appendiceal tumors and their peritoneal metastases. In this article, the most contentious issues in the area of appendiceal mucinous tumors are examined. First, the classification systems that have been proposed for these tumors are compared in the context of whether the appendiceal mucinous tumors are ruptured adenomas or invasive carcinomas. The controversy about the nature of pseudomyxoma peritonei and its classification systems is discussed in the following section. A brief discussion follows that examines the issue of localized pseudomyxoma peritonei and its clinical significance. Next reviewed is the largely resolved controversy about whether ovarian mucinous tumors in this setting are separate primaries or are metastases from the appendiceal tumor. Finally, the controversy about the most effective treatment of patients with pseudomyxoma peritonei is discussed.