Radiomics, the high-throughput extraction of quantitative imaging features from medical images, holds immense potential for advancing precision medicine in oncology and beyond. While radiomics applied to positron emission tomography (PET) imaging offers unique insights into tumor biology and treatment response, it is imperative to elucidate the challenges and constraints inherent in this domain to facilitate their translation into clinical practice. This review examines the challenges and limitations of applying radiomics to PET imaging, synthesizing findings from the last five years (2019-2023) and highlights the significance of addressing these challenges to realize the full clinical potential of radiomics in oncology and molecular imaging. A comprehensive search was conducted across multiple electronic databases, including PubMed, Scopus, and Web of Science, using keywords relevant to radiomics issues in PET imaging. Only studies published in peer-reviewed journals were eligible for inclusion in this review. Although many studies have highlighted the potential of radiomics in predicting treatment response, assessing tumor heterogeneity, enabling risk stratification, and personalized therapy selection, various challenges regarding the practical implementation of the proposed models still need to be addressed. This review illustrates the challenges and limitations of radiomics in PET imaging across various cancer types, encompassing both phantom and clinical investigations. The analyzed studies highlight the importance of reproducible segmentation methods, standardized pre-processing and post-processing methodologies, and the need to create large multicenter studies registered in a centralized database to promote the continuous validation and clinical integration of radiomics into PET imaging.