The virtual, digital counterpart of a physical object, referred as digital twin, derives from the Internet of Things (IoT), and involves real-time acquisition and processing of large data sets. A fully implemented system ultimately enables real-time and remote management, as well as the reproduction of real and forecasted scenarios. Under the emerging framework of Precision Fish Farming, which brings control-engineering principles to fish production, we set up digital twin prototypes for land-based finfish farms. The digital twin is aimed at supporting producers in optimizing feeding practices, oxygen supply and fish population management with respect to 1) fish growth performances; 2) fish welfare, and 3) environmental loads. It relies on integrated mathematical models which are fed with data from in-situ sensors and from external sources, and simulate several dynamic processes, allowing the estimation of key parameters describing the ambient environment and the fishes. A conceptual application targeted at rearing cycles of rainbow trout (Oncorhynchus mykiss) in an operational in-land aquafarm in Italy is presented. The digital twin takes into account the disparate levels of automation and control that are found within this farm, and considerations are made on preferential directions for future developments. In spite of its potential, and not only in the aquaculture sector, the development of digital twins is still at its early stage. Furthermore, Precision Fish Farming applications in land-based systems as well as targeted at rainbow trout are novel developments.