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The high-throughput extraction of quantitative imaging features from medical images for the purpose of radiomic analysis, i.e., radiomics in a broad sense, is a rapidly developing and emerging research field that has been attracting increasing interest, particularly in multimodality and multi-omics studies. In this context, the quantitative analysis of multidimensional data plays an essential role in assessing the spatio-temporal characteristics of different tissues and organs and their microenvironment. Herein, recent developments in this method, including manually defined features, data acquisition and preprocessing, lesion segmentation, feature extraction, feature selection and dimension reduction, statistical analysis, and model construction, are reviewed. In addition, deep learning-based techniques for automatic segmentation and radiomic analysis are being analyzed to address limitations such as rigorous workflow, manual/semi-automatic lesion annotation, and inadequate feature criteria, and multicenter validation. Furthermore, a summary of the current state-of-the-art applications of this technology in disease diagnosis, treatment response, and prognosis prediction from the perspective of radiology images, multimodality images, histopathology images, and three-dimensional dose distribution data, particularly in oncology, is presented. The potential and value of radiomics in diagnostic and therapeutic strategies are also further analyzed, and for the first time, the advances and challenges associated with dosiomics in radiotherapy are summarized, highlighting the latest progress in radiomics. Finally, a robust framework for radiomic analysis is presented and challenges and recommendations for future development are discussed, including but not limited to the factors that affect model stability (medical big data and multitype data and expert knowledge in medical), limitations of data-driven processes (reproducibility and interpretability of studies, different treatment alternatives for various institutions, and prospective researches and clinical trials), and thoughts on future directions (the capability to achieve clinical applications and open platform for radiomics analysis).