The remarkable success of Transformer-based embeddings in natural language tasks has sparked interest among researchers in applying them to classify rumours on social media, particularly microblogging platforms. Unlike traditional word embedding methods, Transformers excel at capturing a word’s contextual meaning by considering words from both the left and right of a word, resulting in superior text representations ideal for tasks like rumour detection on microblogging platforms. This survey aims to provide a thorough and well-organized overview and analysis of existing research on implementing Transformer-based models for rumour detection on microblogging platforms. The scope of this study is to offer a comprehensive understanding of this topic by systematically examining and organizing the existing literature. We start by discussing the fundamental reasons and significance of automating rumour detection on microblogging platforms. Emphasizing the critical role of text embedding in converting textual data into numerical representations, we review current approaches to implement Transformer models for rumour detection on microblogging platforms. Furthermore, we present a novel taxonomy that covers a wide array of techniques and approaches employed in the deployment of Transformer-based models for identifying misinformation on microblogging platforms. Additionally, we highlight the challenges associated with this field and propose potential avenues for future research. Drawing insights from the surveyed articles, we anticipate that promising results will continue to emerge as the challenges outlined in this study are addressed. We hope that our efforts will stimulate further interest in harnessing the capabilities of Transformer models to combat the spread of rumours on microblogging platforms.