Digital twin technologies in manufacturing have evolved into dynamic, data-synchronized systems that facilitate real-time monitoring and control. Given that machining involves closely interconnected multi-physics behaviors, the effectiveness of a digital twin largely relies on the accuracy and reliability of its underlying process models. This review systematically evaluates three primary paradigms for machining process modeling in digital twins: physics-based, data-driven, and hybrid approaches. Physics-based models provide interpretability and physical consistency but are hindered by high computational costs and limited adaptability to changing conditions. In contrast, data-driven models offer real-time capabilities and adaptive learning but face challenges related to data scarcity and black-box behavior. Hybrid modeling has emerged as the most promising approach, combining physical laws with machine learning through techniques such as parameter correction, physics-guided learning, and state-estimation-based intelligent control. Recent research demonstrates significant advancements in predictive performance, adaptability, and computational efficiency across various machining applications, underscoring the effectiveness of new process modeling strategies for digital twins. However, challenges remain, including multi-physics integration, model reduction for real-time deployment, and autonomous self-updating in data-limited scenarios. The review concludes that hybrid models present the most viable pathway to achieving high-fidelity, self-adaptive, and trustworthy digital twins for autonomous manufacturing.