Digital twins represent an established technology in several fields of science and engineering, providing a new paradigm to conceive, design and operate complex systems. The success of these reduced order models (ROM) stems from their capability to solve many-queries problems (e.g., shape optimisation and uncertainty quantification), to integrate physics-based models with data-driven information and to construct virtual prototypes of multidisciplinary -- possibly coupled -- systems, common in industrial and sustainable development settings. One of the major bottlenecks in the construction of these surrogate models -- being projection-based ROMs, a priori proper generalised decomposition (PGD) or physics-informed neural networks -- is represented by the amount of required experimental and/or simulation-based data [1]. The former is usually scarce and the latter is computationally expensive. This issue becomes especially critical when high-dimensional problems involving many parameters and large-scale systems with hundreds of millions of unknowns are involved. In this talk, some recent approaches to reduce the cost of building digital twins are presented. First, a strategy to reduce the size of the high-fidelity simulations required by the ROM is discussed. This approach relies on a domain decomposition rationale: local surrogate models are constructed in an offline phase using PGD and then glued together via an overlapping Schwarz method to be executed in real time [2]. Then, a technique to reduce the number of high-fidelity simulations to devise the ROM is presented: the multi-index stochastic collocation method [3] is employed to construct a multifidelity model capable of adaptively identifying the most suitable snapshots to be incorporated in the ROM, blending simulations of different fidelities obtained using different levels of mesh refinement. The resulting digital twins are applied to solve parametric problems involving different physics, from thermal phenomena to viscous incompressible flows, greatly reducing the computational cost of the corresponding surrogate models constructed using high-fidelity simulations of the full-scale problems.