In this talk, we aim to summarize some recent developments as well as opportunities and challenges in the use of projection-based model order reduction (MOR) for parametrized PDEs in the context of digital twins.  In the first part, we consider the development of (a) reduced-order models (ROMs) for multi-scale problems in solid mechanics and (b) sampling strategies for the construction of ROMs in problems with high-dimensional parameters.  In the second part, we consider challenges in the use of ROMs digital twins, for example in data assimilation, Bayesian inverse problems, and optimal sensor placement.