The move towards advanced manufacturing and Industry 4.0 is fed by increased demand for speeding up innovation, increasing flexibility, improving maintenance, and becoming more customized while saving on the total cost of operations. This is accompanied by increased dependence on virtual product and process development, data‐driven processes, and product knowledge. Other characteristics, affecting modern design, include big data intelligence in product, process, and maintenance. New technologies that empower data analytics include added manufacturing, flexible manufacturing, robotics, sensor technology, smart value/supply chains, and industrial information backbones. This paper is about surrogate models, also called digital twins, that provide an important complementary capacity to physical assets. Digital twins capture past, present, and predicted behavior of physical assets. Digital twin models are updated periodically to represent the current state of physical assets. This distinguishes digital twins from conventional simulations in that sensor data can continuously feed them. The type of curated information on the state of physical asset's history depends on how digital twins are used. For example, if a digital twin is used for fault classification, the history captured is operational data from equipment in healthy and faulty states. We provide here a review of digital twins, with an emphasis on Industry 4.0 applications.