This open access book explores the latest advancements in simulation performance, driven by model order reduction, informed and augmented machine learning technologies and their combination into the so-called hybrid digital twins. It provides a comprehensive review of three key frameworks shaping modern engineering simulations: physics-based models, data-driven approaches, and hybrid techniques that integrate both. The book examines the limitations of traditional models, the role of data acquisition in uncovering underlying patterns, and how physics-informed and augmented learning techniques contribute to the development of digital twins. Organized into four sections—Around Data, Around Learning, Around Reduction, and Around Data Assimilation & Twinning—this book offers an essential resource for researchers, engineers, and students seeking to understand and apply cutting-edge simulation methodologies