Application of polarimetric synthetic aperture radar interferometry to the retrieval of geophysical parameters from vegetated scenes is based on simple direct models of such scenes. The first part of this paper presents an analysis of the correspondence between these simple models, namely, the random volume over ground and the oriented volume over ground (OVoG), and experimental data from samples of two agricultural crops (maize and rice) acquired in controlled conditions. Although an overall agreement between model and data is clear, some discrepancies have been found as a consequence of two assumptions in the model formulation: vertical homogeneity of the vegetation volume and absence of multiple scattering effects inside the volume. This paper presents the shape and location of the visible region of the experimental coherences on the complex plane and compares it with the feasible region predicted by the model. This comparison has also pointed out the low sensitivity of the direct model to extinction coefficients. In the second part, two different strategies for a complete inversion (i.e., estimation of all model parameters) of the OVoG model are proposed and compared, using the same data set. The first one is based on a combination of geometrical and numerical approaches (genetic algorithms) and the second one on a dual-baseline configuration. In all cases, ground topography is accurately estimated, with a maximum error of 10 cm. Vegetation height estimates are accurate up to 30 cm, with some bands and baseline configurations providing errors below 15 cm. However, results obtained for the extinction coefficients are not stable with frequency and exhibit high variability.