The digital twin has recently become a popular topic in research related to manufacturing, such as Industry 4.0, the industrial internet of things, and cyber-physical systems. In addition, digital twins are the focus of several research areas: construction, urban management, digital transformation of the economy, medicine, virtual reality, software testing, and others. The concept is not yet fully defined, its scope seems unlimited, and the topic is relatively new; all this can present a barrier to research. The main goal of this paper is to develop a proper methodology for visualizing the digital-twin science landscape using modern bibliometric tools, text-mining and topic-modelling, based on machine learning models—Latent Dirichlet Allocation (LDA) and BERTopic (Bidirectional Encoder Representations from Transformers). The scope of the study includes 8693 publications on the topic selected from the Scopus database, published between January 1993 and September 2022. Keyword co-occurrence analysis and topic-modelling indicate that studies on digital twins are still in the early stage of development. At the same time, the core of the topic is growing, and some topic clusters are emerging. More than 100 topics can be identified; the most popular and fastest-growing topic is ‘digital twins of industrial robots, production lines and objects.’ Further efforts are needed to verify the proposed methodology, which can be achieved by analyzing other research fields.