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Ultra-Precision Machining (UPM) is a kind of highly accurate processing technology developed to satisfy the manufacturing requirements of high-end cutting-edge products including nuclear energy producers, very large-scale integrated circuits, lasers, and aircraft. The information asymmetry phenomenon widely exists in the design and control of ultra-precision machining. It may lead to inconsistency between the designed performance and operational performance of the UPM equipment on stiffness, thermal stability, and motion accuracy, which result from its design, manufacturing, and control, and determine the form accuracy and surface roughness of machined parts. The performance of the UPM equipment should be improved continuously. It is still challenging to realize the real-time and self-adaptive control, in which building a high-fidelity and computationally efficient digital twin is a valuable solution. Nevertheless, the incorporation of the digital twin technology into the UPM design and control remains vague and sometimes contradictory. Based on a literature search in the Google Scholar database, the critical issues in the UPM design and control, and how to use the digital twin technologies to promote it, are reviewed. Firstly, the digital twins-based UPM design, including bearings module design, spindle-drive module design, stage system module design, servo module design, and clamping module design, are reviewed. Secondly, the digital twins-based UPM control studies, including voxel modeling, process planning, process monitoring, vibration control, and quality prediction, are reviewed. The key enabling technologies and research directions of digital twins-based design and control are discussed to deal with the information asymmetry phenomenon in UPM. [ABSTRACT FROM AUTHOR]