Aortic valve defects are among the most prevalent clinical conditions. A severely damaged or non-functioning aortic valve is commonly replaced with a bioprosthetic heart valve (BHV) via the transcatheter aortic valve replacement (TAVR) procedure. Accurate pre-operative planning is crucial for a successful TAVR outcome. Assessment of computational fluid dynamics (CFD), finite element analysis (FEA), and fluid–solid interaction (FSI) analysis offer a solution that has been increasingly utilized to evaluate BHV mechanics and dynamics. However, the high computational costs and the complex operation of computational modeling hinder its application. Recent advancements in the deep learning (DL) domain can offer a real-time surrogate that can render hemodynamic parameters in a few seconds, thus guiding clinicians to select the optimal treatment option. Herein, we provide a comprehensive review of classical computational modeling approaches, medical imaging, and DL approaches for planning and outcome assessment of TAVR. Particularly, we focus on DL approaches in previous studies, highlighting the utilized datasets, deployed DL models, and achieved results. We emphasize the critical challenges and recommend several future directions for innovative researchers to tackle. Finally, an end-to-end smart DL framework is outlined for real-time assessment and recommendation of the best BHV design for TAVR. Ultimately, deploying such a framework in future studies will support clinicians in minimizing risks during TAVR therapy planning and will help in improving patient care.