Accurate and timely estimation of rice canopy height is crucial for crop monitoring, yield forecasting, lodging assessment and precision agriculture. Optical remote sensing is frequently constrained by cloud cover during the monsoon-aligned rice cultivation period. Synthetic aperture radar (SAR) and Polarimetric SAR Interferometry (Pol-InSAR) offer a physically grounded route to canopy structure by using the polarimetric scattering mechanisms, traditionally formalised through the random volume over ground (RVoG) model approach. This review synthesises the basic principles of the Pol-InSAR approach for vegetation height measurements and the effects of unique rice scattering mechanisms caused by the existence of a water layer under the canopy, which impose on the classical assumptions of the RVoG approach. Recent machine learning (ML) approaches provide an overview of applications, including random forest and support vector regression, in conjunction with Pol-InSAR and PolSAR data. Key persistent challenges include temporal decorrelation, water-layer phase centre ambiguity and limited cross-site applicability of the models, including physics-informed hybrid ML models, multisensors/multiband fusion and operational monitoring approaches. This review argues that combining the use of the combination of Pol-InSAR physical foundation and ML modelling is the most promising path forward.