Radiomics describes a broad set of computational methods that extract quantitative features from radiographic images. The resulting features can be used to inform imaging diagnosis, prognosis, and therapy response in oncology. However, major challenges remain for methodological developments to optimize feature extraction and provide rapid information flow in clinical settings. Equally important, to be clinically useful, predictive radiomic properties must be clearly linked to meaningful biological characteristics as well as qualitative imaging properties familiar to radiologist. Here we use a cross-disciplinary approach to highlight studies in radiomics. We review brain tumor radiological studies (e.g., imaging interpretation) through computational models (e.g., computer vision and machine learning) that provide novel clinical insights. In particular, we outline current quantitative image feature extraction and prediction strategies with different level of available clinical classes for supporting clinical decision making. We further discuss machine learning challenges and data opportunities to advance radiomic studies.