Recently, significant efforts have been made to create Health Digital Twins (HDTs), Digital Twins for clinical applications. Heart modeling is one of the fastest-growing fields, which favors the effective application of HDTs. The clinical application of HDTs will be increasingly widespread in the future of healthcare services and has huge potential to form part of mainstream medicine. However, it requires the development of both models and algorithms for the analysis of medical data, and advances in Artificial Intelligence (AI)-based algorithms have already revolutionized image segmentation processes. Precise segmentation of lesions may contribute to an efficient diagnostics process and a more effective selection of targeted therapy. In this systematic review, a brief overview of recent achievements in HDT technologies in the field of cardiology, including interventional cardiology, was conducted. HDTs were studied taking into account the application of Extended Reality (XR) and AI, as well as data security, technical risks, and ethics-related issues. Special emphasis was put on automatic segmentation issues. In this study, 253 literature sources were taken into account. It appears that improvements in data processing will focus on automatic segmentation of medical imaging in addition to three-dimensional (3D) pictures to reconstruct the anatomy of the heart and torso that can be displayed in XR-based devices. This will contribute to the development of effective heart diagnostics. The combination of AI, XR, and an HDT-based solution will help to avoid technical errors and serve as a universal methodology in the development of personalized cardiology. Additionally, we describe potential applications, limitations, and further research directions.