Training effective artificial intelligence models for telecommunications is challenging due to the scarcity of deployment-specific data. Real data collection is expensive, and available datasets often fail to capture the unique operational conditions and contextual variability of the network environment. Digital twinning provides a potential solution to this problem, as simulators tailored to the current network deployment can generate site-specific data to augment the available training datasets. However, there is a need to develop solutions to bridge the inherent simulation-to-reality (sim-to-real) gap between synthetic and real-world data. This paper reviews recent advances on two complementary strategies: 1) the calibration of digital twins (DTs) through real-world measurements, and 2) the use of sim-to-real gap-aware training strategies to robustly handle residual discrepancies between digital twin-generated and real data. For the latter, we evaluate two conceptually distinct methods that model the sim-to-real gap either at the level of the environment via Bayesian learning or at the level of the training loss via prediction-powered inference.