Being able to penetrate clouds and fog, Synthetic Aperture Radar (SAR) imagery has been widely used in flood mapping and flood detection regardless of time and weather condition. Improving the accuracy of flood maps retrieved from SAR images is of both scientific and practical significance. However, errors in SAR-derived flood maps can come from SAR image measuring principles, image acquisition and pre-processing system, water detection algorithms, and the remarkable temporal dynamics of the flooding process. The aim of this paper is to provide an extensive literature review of flood detection using SAR images (about 108 peer reviewed journal papers), including SAR data sources, flood detection methods, application of auxiliary information, accuracy evaluation, and challenges and opportunities for future research. Based on the articles reporting flood detection methods, it is found that the threshold segmentation methods such as the OTSU and KI algorithms are computationally fast and have been most widely used. The classification methods (e.g., the support vector machine and K-means clustering algorithms) have the flexibility to account for both subjectivity and objectivity, and the change detection method using the difference and ratio algorithms can effectively suppress over-detection and image geometric errors. Additionally, combining SAR images with four major types of auxiliary data to increase flood detection accuracy has become a hot topic in the past decades. Specifically, terrain information such as Digital Elevation Model (DEM), Height Above Nearest Drainage (HAND), and topographic slope can effectively reduce the impacts of shadows and exclude non-flooded areas. SAR image textural and multispectral optical information (e.g., Landsat data and aerial photos) can enhance the recognition ability of water features. Land cover/use data facilitate removing non-water features that are similar to water features, and hydrological data can help excluding permanent water bodies from temporary flood areas. From the perspectives of SAR image types, image preprocessing, detection algorithms, and accuracy assessment, major challenges are further discussed including insufficient understanding of the complexity of SAR backscattering information, limited progress in improving the signal-to-noise ratio during image pre-processing, lack of versatile flood detection algorithms, and low availability of high-quality verification data. While opportunities for future SAR-based flood detection research include combination of auxiliary information in detection algorithms, use of multiple rather than single threshold for water detection, and transition from deterministic toward probabilistic flood mapping.