Machine Translation Quality Estimation (MTQE) is the task of estimating the quality of machine-translated text in real time without the need for reference translations, which is of great importance for the development of MT. After two decades of evolution, QE has yielded a wealth of results. This article provides a comprehensive overview of QE datasets, annotation methods, shared tasks, methodologies, challenges, and future research directions. It begins with an introduction to the background and significance of QE, followed by an explanation of the concepts and evaluation metrics for word-level QE, sentence-level QE, document-level QE, and explainable QE. The paper categorizes the methods developed throughout the history of QE into those based on handcrafted features, deep learning, and Large Language Models (LLMs), with a further division of deep learning-based methods into classic deep learning and those incorporating pre-trained language models (LMs). Additionally, the article details the advantages and limitations of each method and offers a straightforward comparison of different approaches. Finally, the paper discusses the current challenges in QE research and provides an outlook on future research directions.

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