Synthetic Aperture Radar (SAR) has been widely used for Earth remote sensing for more than 30 years. It provides high-resolution, day-and-night and weather-independent images for a multitude of applications ranging from geoscience and climate change research, environmental and Earth system monitoring, 2-D and 3-D mapping, change detection, 4-D mapping (space and time), security-related applications up to planetary exploration. With the advances in radar technology and geo/bio-physical parameter inversion modeling in the 90s, using data from several airborne and spaceborne systems, a paradigm shift occurred from the development driven by the technology push to the user demand pull. Today, more than 15 spaceborne SAR systems are being operated for innumerous applications. This paper provides first a tutorial about the SAR principles and theory, followed by an overview of established techniques like polarimetry, interferometry and differential interferometry as well as of emerging techniques (e.g., polarimetric SAR interferometry, tomography and holographic tomography). Several application examples including the associated parameter inversion modeling are provided for each case. The paper also describes innovative technologies and concepts like digital beamforming, Multiple-Input Multiple-Output (MIMO) and bi- and multi-static configurations which are suitable means to fulfill the increasing user requirements. The paper concludes with a vision for SAR remote sensing.