Digital twins are complex software systems that accompany cyber-physical systems. Their engineering involves challenging research topics to address system, time, integration, and information complexity. Modeling techniques help master the complexity of long-living systems, and combined with generative methods, models of cyber-physical systems can be used for digital twin engineering and evolution. Thus, it is essential to investigate how model-driven engineering methods can be applied and improved so that they are applicable and beneficial for digital twin engineering. This thesis summarizes 9 selected publications of a research program towards the application and improvement of model-driven methods for the engineering of digital twins. Digital twins encompass a diverse range of services, e.g., data collection, aggregation, analysis, prediction, execution, information, and assistance. Moreover, digital twins from different domains share similarities, such as their reliance on sensory information as supplemental data sources, connections to third-party applications for additional information, requiring data-intensive operations and visualizations, and utilizing models derived from data during runtime. Architectural components systematically capture these functionalities. We have explored how to describe such architectural components to be usable and reusable for model-driven engineering. Additionally, we have investigated how model-driven engineering can be applied to derive parts of digital twins, determining the use of both general-purpose and domain-specific modeling languages for their engineering and execution. This work contributes to an improved development of digital twins for complex, long-living systems with foundations, concepts, and methods.