The Digital Twin (DT) term is currently used, sometimes as a buzzword, to refer to a virtual representation or digital replica of a physical object, process, or system. DTs have the potential to improve efficiency, reduce costs, and enhance decision-making, in particular if they are not limited to just providing digital shadows of their physical counterparts, but are employed in their full capability to act/react on them via commands and re-configurations, thus enabling an efficient runtime control feedback loop. Even if DTs have already started to demonstrate their suitability for several application fields, e.g., from smart energy to intelligent transportation, our experience in several EU/national research projects has pointed out that some related hard technical challenges have still to be satisfyingly solved. This is particularly true for the effective adoption of DTs in i) industrial deployment environments with stringent latency requirements and ii) very open and wide-scale smart city scenarios. The paper aims to distill the lessons learned about those DT challenges and present our Cloud Continuum DTs concept. More specifically, on the one hand, the paper describes the architectural principles, the model, and the primary design/implementation choices we took in our Cloud Continuum DT support platform. On the other hand, we will focus on the hard technical challenge of ultra-low-latency DTs by presenting our related middleware that is the basis of our Cloud Continuum DT platform when deployed for industrial and automation control execution environments.