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Synthetic aperture radar interferometry (InSAR) is a powerful and increasingly expanding technique for measuring the topography of a surface, its changes over both short- and long-time scale, and other changes in the detailed characteristics of the surface. We provide a tutorial description of recent results on multibaseline (MB) InSAR processing. The main focus is on the problem of retrieving both heights and radar reflectivities of natural layover areas by means of a cross-track InSAR (XTI-SAR) system with a uniform linear array (ULA). It is formulated as the problem of detecting and estimating a multicomponent signal corrupted by multiplicative noise - the speckle in the radar imaging jargon - and by additive white Gaussian noise. Application to the InSAR problem of both nonparametric and parametric modern spectral estimation techniques is described. The problem of estimating the number of signal components in the presence of speckle is also addressed. Finally, a brief mention is given to recent research trends on robust methods for nonperfectly calibrated arrays, on processing for non-ULA configurations, and on MB SAR tomography, which is an extension of MB SAR interferometry for the full 3D mapping of semitransparent volume scattering layers. The state of the art of other advanced multichannel interferometric techniques is also briefly recalled.