Although quantitative image biomarkers (radiomics) show promising value for cancer diagnosis, prognosis, and treatment assessment, these biomarkers still lack reproducibility. In this systematic review, we aimed to assess the progress in radiomics reproducibility and repeatability in the recent years. Four hundred fifty-one abstracts were retrieved according to our search pattern criteria, with the publication dates ranging from 2017/05/01 to 2020/12/01. Each abstract including the keywords was independently screened by four observers. Forty-two full-text articles were selected for further analysis. Patient population data, radiomic feature classes, feature extraction software, image preprocessing, and reproducibility results were extracted from each article. To support the community with a standardized reporting strategy, we propose a specific reporting checklist to evaluate the feasibility to reproduce each study. Many studies continue to under-report essential reproducibility information: all but one clinical and all but two phantom studies missed to report at least one important item reporting image acquisition. The studies included in this review indicate that all radiomic features are sensitive to image acquisition, reconstruction, tumor segmentation, and interpolation. However, the amount of sensitivity is feature dependent, for instance, textural features were, in general, less robust than statistical features. Radiomics repeatability, reproducibility, and reporting quality can substantially be improved regarding feature extraction software and settings, image preprocessing and acquisition, cutoff values for stable feature selection. Our proposed radiomics reporting checklist can serve to simplify and improve the reporting and, eventually, guarantee the possibility to fully replicate and validate radiomic studies.