We present Flow Map Learning (FML), a data driven modeling framework, for Digital Twin modeling, simulation and control in real-time. This framework enables the construction of accurate predictive models for complex systems even when governing equations are unavailable. FML is particularly powerful in the context of Digital Twins, as it enables the construction of simulation models for key quantities of interest (QoIs) when direct mathematical modeling is impossible. During online execution of a Digital Twin, the learned FML model can simulate the QoIs without reverting to the computationally intensive full Digital Twin simulations. As a result, FML serves as an enabling methodology for real-time control and optimization for complex systems.