This article presents a systematic literature survey on model-based digital twin engineering (MBDTE). We introduce a novel taxonomy for categorizing MBDTE approaches and provide definitions of both MBDTE and the models it employs. Model-based engineering (MBE) leverages models as essential pillars of the development process, enabling teams to clarify requirements, streamline design, specify behavior, and perform rigorous verification and validation across the entire system life cycle. Digital twins (DTs) are software systems that mirror cyber-physical, socio-economic, or biological entities, systems, or processes. Built from models and data, DTs support high-impact applications including planning, monitoring, control, and optimization of their physical counterparts. The model-centric nature of DTs has naturally sparked exploration into harnessing MBE for DT engineering and operation. However, this exploration for now has created a fragmented landscape of partial solutions. To address this challenge, our survey analyzes 47 peer-reviewed publications across four dimensions, viz., model characteristics, data integration, implementation technologies, and empirical evidence, to map the current state of practice, identify critical research gaps, and avenues for further exploration.