Digital twins have gained a lot of interest in recent years. This paper presents a survey among researchers and engineers with expertise in variation management confirming the interest of digital twins in this area. The survey shows, however, a gap between future research interest in academia and industry, identifying a larger need in industry. This indicates that there are some barriers in the industry to overcome before the benefits of a digital twin for variation management and geometry assurance can be fully capitalized on in an industrial context. To identify those barriers and challenges, an extensive interview study with engineers from eight different companies in the manufacturing sectors was accomplished. The analysis identifies industrial challenges in the areas of system-level, simulation working process, management issues, and education. One of the main challenges is to keep the 3D models fully updated, including keeping track of changes during the product development process and also feedback changes during full production to the development engineers. This is a part of what is called the digital thread, which is also addressed in this paper.