To appear in IEEE Transactions on Industrial Informatics Abstract: Although the skills of robot manipulators are becoming technically more complex, the unprecedented cost-effective access to recently unveiled intelligent robots has the potential to unleash as yet unimagined automation capabilities. A key technology behind this opportunity for companies to gain a competitive edge through an informed and intelligent robotized automation is the robotic digital twin (RDT). As such, the RDT will be instrumental in mirroring targeted properties of a physical robot to obtain a digital sibling flexibly harnessed in virtual testbeds to understand, predict, and shape the robot performance. However, these objectives remain challenging to well-established simulators. This is because the architectural and functional capabilities they support are not sufficiently in-line with ever-growing and varying demands for agile and cost-efficient manipulations. As a consequence, robot stakeholders can hardly use RDTs to unlock opportunities and meet needs from prospective markets. This paper contributes to addressing this gap. We introduce a novel concept for the development of a RDT that helps create and add value to current and future robotized cyber-physical applications. Hereinafter referred to as the value-driven RDT (vdRDT), it systematically captures the robot dynamics and purposefully farms data, about which its services reason to facilitate insight and deliver capabilities and benefits to stakeholders. Experiment results show that vdRDTs enlarge the scope of, adapt to, and revitalize robotized applications carried out in different fields.