## 1 Introduction  
The diagnosis and treatment of aortic diseases is performed in accordance with clinical guidelines provided by several organisations, such as the American Heart Association, American College of Cardiology and European Society of Cardiology [1, 2]. The treatment guidelines for Ascending Thoracic Aortic Aneurysm (ATAA) and Abdominal Aortic Aneurysm (AAA) suggest surgical intervention for patients with a maximum diameter greater than 55 mm. This simple geometrical criterion is supported by Laplace's law and empirical evidence of a significant increase in rupture risk from 0.6% to 6.9% in aortaswith 50 mm and 60 mm diameters, respectively [3]. This criterion, although clinically still accepted and used, is also controversial and is now extensively recognised as insufficient [4; 5]. For instance, [PERSON] et al. [6] showed that around 13% of ATAA occurs with an aortic size below 50 mm rupture, whereas 54% of those over 70 mm may not rupture over long periods. Therefore, these findings reveal an unmet clinical need for suitable, robust and accurate risk assessment metrics that will assist clinicians in clinical diagnosis and decision making.  
The development of patient-specific computational models assisted by in vivo data obtained via non-invasive measurements that could mimic the biomechanical behaviour of Cardiovascular Diseases (CVD) in the framework of a digital twin platform has been presented as adding value to clinical examination [7; 8]. These models are able to provide clinicians with insightful in vivo patient-specific data, such as Wall Shear Stress (WSS) and pressure distributions, displacement field, intramural stress state or flow patterns, which are otherwise unavailable. Over the last few decades, these advanced computational models and simulation tools have also enabled a better understanding of the underlying mechanisms of a variety of CVD, including aortic aneurysms and dissection. Several computational techniques, such as the Finite Element Method (FEM), Machine Learning (ML) and Smoothed Particle Hydrodynamics (SPH), have been applied. These techniques, spanning the entire range of numerical approaches, encompass Computational Solid Mechanics (CSM) and Computational Fluid Dynamics (CFD) to Fluid-Structure Interaction (FSI). CSM is useful to study the Wall Stress (WS) distributions and deformations [9; 10]. CFD solves the governing equations of fluid mechanics and studies haemodynamics patterns and metrics [11; 12]. FSI combines the above-mentioned approaches and simultaneously evaluates haemodynamics and wall motion [13; 14]. Such studies did not specifically address the impact of considering the heterogeneity of wall thickness and material properties, the effect of surrounding structures and the aortic root motion at applying the numerical tools. Exploring the limitations of current numerical models that are constraining their introduction into clinical practice, and providing an extensive overview of the utilised numerical techniques to reproduce aortic biomechanics, are the main goals of this review.  
In this article, a systematic review following the PRISMA [15] methodology is presented, concerning the computational modelling and simulation of the biomechanical behaviour of healthy and diseased aortas, and we explore their methodologies, hypotheses and risk evaluation metrics in view of their usage in clinical practice in order to answer the following scientific questions: \"Which mathematical models have been applied to simulate the biomechanical behaviour of healthy and diseased aortas?\" and \"Why are these models not clinically implemented?\". Section 2 explains how the search, selection and screening processes were performed. In Section 3, a summary of the selected articles is presented, and in Section 4, the raised questions are discussed. Finally, in Section 5, a summary of the systematic review is given.