Digital twin (DT), primarily a virtual replica of any conceivable physical entity, is a highly transformative technology with profound implications. Whether it be product development, design optimisation, performance improvement, or predictive maintenance, digital twins are changing the ways work is undertaken in various industries with multifarious business applications. Aerospace industry, including its manufacturing base, is one such keen adopter of digital twins with an unprecedented interest in their bespoke design, development, and implementation across wider operations and critical functions. This, however, comes with some misconceptions about the digital twin technology and lack of understanding with respect to its optimal implementation. For instance, equating a digital twin to an intelligent model while ignoring the essential components of data acquisition and visualisation, misleads the creators into building digital shadow or digital models, instead of the actual digital twin. This paper unfolds such intricacies of digital twin technology for the aerospace community in particular and others in general so as to remove the fallacies that affect their effective realisation for safety-critical systems. It comprises a comprehensive survey of digital twins and their constituent elements. Elaborating their characteristic state-of-the-art composition along with corresponding limitations, three dimensions of the future digital twins for the aerospace sector, termed as aero-Digital Twins (aero-DTs), are proposed as an outcome of this survey. These include the interactive, standardisation, and cognitive dimensions of digital twins, which if leveraged diligently could help the aero-DT research and development community quadruple the efficiency of existing and future aerospace systems as well as their associated processes.