Subsurface microwave tomography brings inverse-scattering ideas into ground-penetrating radar and related near-surface sensing problems. The field has developed around a central tension: the need to model lossy soil, the air-soil interface, clutter, and antenna effects realistically, while keeping the inverse problem stable enough for practical imaging. This tutorial review organizes the literature around that tension. It first explains the microwave measurement principle behind subsurface imaging, then surveys the main method families: linear diffraction or Born tomography, nonlinear inverse scattering, full-waveform inversion, sparse radio-frequency tomography, contactless sensing, and hybrid radar-tomography workflows. The review argues that the most defensible default for general buried-object imaging remains surface-based multistatic acquisition with an interface-aware linear half-space model and regularized linear inversion. Nonlinear inversion and full-waveform inversion become appropriate when quantitative dielectric characterization justifies stronger modeling assumptions and higher computational cost. Sparse RF tomography and contactless or hybrid methods are best understood as extensions for wide-area, limited-access, or constrained-view settings rather than replacements for the core workflow. The aim is not to exhaust every branch of the literature, but to give new entrants a coherent conceptual map of how measurement, hardware, and inversion fit together in subsurface microwave imaging. Note: This is a preprint of a manuscript submitted to an IEEE journal.
Baidillah et al. (Mon,) studied this question.