Since their introduction in the Eighties, coronary stents have undergone significant design improvements, making them a critical tool for treating severe obstructions. From original Bare-Metal Stents (BMS) to Drug Eluting Stents (DES) to the most recent experience of Bioresorbable Stents, the design of these scaffolds was minimally supported by mathematical tools. The patient-specific quantitative analysis of stented coronaries is a difficult task for the variety of complex morphologies left by the stent deployment. Therefore, this type of analysis was limited to a minimal number of patients, not compatible with clinical trials. On the other hand, the development and the failure of Brioresorbable Stents clearly pointed out the importance of rigorous quantitative tools in the design of next-generation scaffolds. In this talk, we will present recent results in investigating coronary stents based on Applied Mathematics (as opposed to traditional animal models). We will consider in detail (i) the modeling of the elution in a multidomain problem solved by iterative substructuring methods involving simultaneously the lumen, the wall, and the struts of the stents; (2) the impact of the struts on the wall shear stress of a significant number of patients; (3) the consequent role of shape optimization and model order reduction in the design of scaffolds. This journey through a sophisticated combination of data and models will pinpoint the critical role of applied mathematics and scientific computing not only for a basic understanding of the biomechanics of stents but also for the clinical routine and the design of more performing prostheses.