Accelerated by the increasing attention drawn by 5G, 6G, and Internet of Things applications, communication and sensing technologies have rapidly evolved from millimeter-wave (mmWave) to terahertz (THz) in recent years. Enabled by significant advancements in electromagnetic (EM) hardware, mmWave and THz frequency regimes spanning 30 GHz to 300 GHz and 300 GHz to 3000 GHz, respectively, can be employed for a host of applications. The main feature of THz systems is high-bandwidth transmission, enabling ultra-high-resolution imaging and high-throughput communications; however, challenges in both the hardware and algorithmic arenas remain for the ubiquitous adoption of THz technology. Spectra comprising mmWave and THz frequencies are well-suited for synthetic aperture radar (SAR) imaging at sub-millimeter resolutions for a wide spectrum of tasks like material characterization and nondestructive testing (NDT). This article provides a tutorial review of systems and algorithms for THz SAR in the near-field with an emphasis on emerging algorithms that combine signal processing and machine learning techniques. As part of this study, an overview of classical and data-driven THz SAR algorithms is provided, focusing on object detection for security applications and SAR image super-resolution. We also discuss relevant issues, challenges, and future research directions for emerging algorithms and THz SAR, including standardization of system and algorithm benchmarking, adoption of state-of-the-art deep learning techniques, signal processing-optimized machine learning, and hybrid data-driven signal processing algorithms...