Recent flood events have demonstrated a demand for satellite-based inundation mapping in near real-time (NRT). Simulating and forecasting flood extent is essential for risk mitigation. While numerical models are designed to provide such information, they usually lack reference at fine spatiotemporal resolution. Remote sensing techniques are expected to fill this void. Unlike optical sensors, synthetic aperture radar (SAR) provides valid measurements through cloud cover with high resolution and increasing sampling frequency from multiple missions. This study reviews theories and algorithms of flood inundation mapping using SAR data, together with a discussion of their strengths and limitations, focusing on the level of automation, robustness, and accuracy. We find that the automation and robustness of non-obstructed inundation mapping have been achieved in this era of big earth observation (EO) data with acceptable accuracy. They are not yet satisfactory, however, for the detection of beneath-vegetation flood mapping using L-band or multi-polarized (dual or fully) SAR data or for urban flood detection using fine-resolution SAR and ancillary building and topographic data.