Digital Twinning (DT) has become a main instrument for Industry 4.0 and the digital transformation of manufacturing and industrial processes. In this statement paper, we elaborate on the potential of Digital Twinning as a valuable tool in support of the management of intelligent infrastructures throughout all stages of their life-cycle. We highlight the associated needs, opportunities and challenges and discuss the needs from both the research and applied perspectives. We elucidate the transformative impact of digital twin applications for strategic decision making, discussing its potential for situation awareness, as well as enhancement of system resilience, with a particular focus on applications that necessitate efficient, and often real-time, or near real-time, diagnostic and prognostic processes. In doing so we elaborate on the separate classes of DT, ranging from simple images of a system, all the way to interactive replicas that are continually updated to reflect a monitored system at hand. We root our approach in the adoption of hybrid modelling as a seminal tool for facilitating twinning applications. Hybrid modelling refers to the synergistic use of data with models that carry engineering or empirical intuition on the system's behaviour. We postulate that modern infrastructures can be viewed as cyber-physical systems comprising, on the one hand, an array of heterogeneous data of diversified granularity and, on the other, a model (analytical, numerical, or other) that carries information on the system's behaviour. We thus propose Hybrid Digital Twins (HDT) as the main enabler of smart and resilient infrastructures.