Distributed digital twins are designed to enhance the intelligence, predictability, and optimization of industrial assets by actively engaging, synchronizing, and collaborating with their physical counterparts, i.e., the systems they model, in near real time. This interoperability allows for seamless connections between real systems and their virtual counterparts, thereby facilitating the flow of data while aggregating vital information for comprehensive insights across large entities. However, the constant exchange of data and dependency on the information technology and operations technology process integrations in the digital twin give rise to various cybersecurity challenges. These include threats to data, unauthorized accesses, as well as threats to the integrity and reliability of the digital tools and the services they offer, among others. In this paper, we discuss the relevant cyberthreats within digital twins ecosystems, which we then analyze while outlining different strategies to mitigate such threats. As a result, we present key takeaways toward a secure and reliable digital twin platform. Finally, different challenges are raised to highlight the status quo on the security of digital twins and areas for improvement.