A digital twin is a virtual model of a system or process that mutually exchanges data with the real counterpart: it progressively adapts and specializes by learning from the physical twin and provides predictions of specific quantities of interest in return. The time- and resource-efficiency requirements impose digital twins of a given physical system or process not to be unique, but rather multifaceted and purpose-driven adaptive models. Accordingly, we advocate that there is not such a twin that rules them all and that rigorous mathematical methods are essential to their formalization for applications to science and engineering [1]. Based on the definitions proposed by different scientific communities [2, 3, 4, 5], we will look into the concept of digital twin matured over the years and discuss its distinguishing features by undertaking a journey along the lifecycle of a system or process. Considerations will be drawn from examples across different engineering domains with particular attention to the challenges introduced at design, maintenance and operations stages.