Reduced and real-time modelling is one of the main pillars of digital “process models” for twinning of manufacturing processes. Starting from the data processing and model building, a digital twin of additive manufacturing (AM) processes involves creating virtual replica where predictions and corrections can be made in real-time. Developing such fast predictive/corrective digital models involve data training and machine learning (ML) routines, where dynamic and accurate models can be employed for process optimisation and control. In this research work, the overview of the real-time modelling and ML data training have been presented for AM processes using hybrid and reduced order modelling (ROM) techniques. Hence, variations of processing parameters (e.g., temperature, power and feeding speed) for wire arc AM processes are considered to develop a tailored process data base and its associated snapshot matrix. Furthermore, the accuracy and reliability of these digital models for monitoring and optimizing AM processes are investigated using a real-world case study. The performances of different reduced model building, and data interpolation techniques have subsequently been scrutinized to create the most accurate and efficient solver-interpolator combinations for integration of real-time models into digital twins for AM processes.