The aim of the present review was to assess the current status of positron emission tomography/computed tomography (PET/CT) radiomics research in breast cancer, and in particular to analyze the strengths and weaknesses of the published papers in order to identify challenges and suggest possible solutions and future research directions. Various combinations of the terms "breast", "radiomic", "PET", "radiomics", "texture", and "textural" were used for the literature search, extended until 8 July 2019, within the PubMed/MEDLINE database. Twenty-six articles fulfilling the inclusion/exclusion criteria were retrieved in full text and analyzed. The studies had technical and clinical objectives, including diagnosis, biological characterization (correlation with histology, molecular subtypes and IHC marker expression), prediction of response to neoadjuvant chemotherapy, staging, and outcome prediction. We reviewed and discussed the selected investigations following the radiomics workflow steps related to the clinical, technical, analysis, and reporting issues. Most of the current evidence on the clinical role of PET/CT radiomics in breast cancer is at the feasibility level. Harmonized methods in image acquisition, post-processing and features calculation, predictive models and classifiers trained and validated on sufficiently representative datasets, adherence to consensus guidelines, and transparent reporting will give validity and generalizability to the results.