In this paper, we present a survey on the progress of radiogenomics research, which predicts cancer genotypes from imaging phenotypes and investigates the associations between them. First, we present an overview of the popular technology modalities for obtaining diagnostic medical images. Second, we summarize recently used methodologies for radiogenomics analysis, including statistical analysis, radiomics and deep learning. And then, we give a survey on the recent research based on several types of cancers. Finally, we discuss these studies and propose possible future research directions. In conclusion, we have identified strong correlations between cancer genotypes and imaging phenotypes. In addition, with the rapid growth of medical data, deep learning models show great application potential for radiogenomics.