Synthetic aperture radar (SAR) tomography (TomoSAR) is an emerging technology to image the 3D structure of the illuminated media. TomoSAR exploits the key feature of microwaves to penetrate into vegetation, snow, and ice, hence providing the possibility to see features that are hidden to optical and hyper-spectral systems. The research on the use of P-band waves, in particular, has been largely propelled since 2007 in experimental studies supporting the future spaceborne Mission BIOMASS, to be launched in 2022 with the aim of mapping forest aboveground biomass (AGB) accurately and globally. The results obtained in the frame of these studies demonstrated that TomoSAR can be used for accurate retrieval of geophysical variables such as forest height and terrain topography and, especially in the case of dense tropical forests, to provide a more direct link to AGB. This paper aims at providing the reader with a comprehensive understanding of TomoSAR and its application for remote sensing of forested areas, with special attention to the case of tropical forests. We will introduce the basic physical principles behind TomoSAR, present the most relevant experimental results of the last decade, and discuss the potentials of BIOMASS tomography.