A digital twin (DT) is a computational model that evolves over time to persistently represent the structure, behavior, and context of a unique physical system or process. DTs are characterized by a dynamic and continuous two-way flow of information between the computational model and the physical system. Data streams from the physical system are assimilated into the computational model to reduce uncertainties and improve model predictions, which in turn are used as a basis for controlling the physical system, optimizing data acquisition, and providing decision support. The DT must execute rapidly enough to support decisions and controls in time scales relevant to the physical system, and must manage and quantify uncertainties across its lifecycle. Often this necessitates DT-aware reduced order or surrogate models, i.e. those that map uncertain parameters, decision variables, and current states to quantities of interest. This minisymposium will focus on mathematical, statistical, and computational foundations underlying DTs, in particular addressing challenges in (1) data assimilation and statistical inverse problems, (2) optimal control and decision making, (3) optimal experimental design, and (4) model reduction and surrogates, all in the context of DTs of complex systems.