Monitoring snowpack depth is essential in many applications at regional and global scales. Space-borne passive microwave (PMW) remote sensing observations have been widely used to estimate snow depth (SD) information for over four decades due to their responsiveness to snowpack characteristics. Many approaches comprised of static and dynamic empirical models, non-linear, machine-learning-based models, and assimilation approaches have been developed using spaceborne PMW observations. These models cannot be applied uniformly over all regions due to inherent limitations in the modelling approaches. Further, the global PMW SD products have masked out in their coverage critical regions such as the Himalayas, as well as very high SD regions, due to constraints triggered by prevailing topographical and snow conditions. Therefore, the current review article discusses different models for SD estimation, along with their merits and limitations. Here in the review, various SD models are grouped into four types, i.e., static, dynamic, assimilation-based, and machine-learning-based models. To demonstrate the rationale behind these drawbacks, this review also details various causes of uncertainty, and the challenges present in the estimation of PMW SD. Finally, based on the status of the available PMW SD datasets, and SD estimation techniques, recommendations for future research are included in this article.