  Digital Twins are one of the hottest digital trends. In this contribution we
will shortly review the concept of Digital Twins and the chances for novel
industrial applications. Mathematics are a key enabler and the impact will be
highlighted along four specific examples addressing Digital Product Twins
democratizing Design, Digital Production Twins enabling robots to mill, Digital
Production Twins driving industrialization of additive manufacturing, and
Digital Performance Twins boosting operations. We conclude the article with an
outlook on the next wave of Digital Twins, Executable Digital Twins, and will
review the associated challenges and opportunities for mathematics.
