Transformer technologies, like generative pre-trained transformers (GPTs) and bidirectional encoder representations from transformers (BERT) are increasingly utilized for understanding diverse social media content. Despite their popularity, there is a notable absence of a systematic literature review on their application in disaster analytics. This study investigates the utilization of transformer-based technology in analyzing social media data for disaster and emergency crisis events. Leveraging a systematic review methodology, 114 related works were collated from popular databases like Web of Science and Scopus. After deduplication and following the exclusion criteria, 53 scholarly articles were analyzed, revealing insights into the geographical distribution of research efforts, trends in publication output over time, publication venues, primary research domains, and prevalently used technology. The results show a significant increase in publications since 2020, with a predominant focus on computer science, followed by engineering and decision sciences. The results emphasize that within the realm of social-media-based disaster analytics, BERT was utilized in 29 papers, BERT-based methods were employed in 28 papers, and GPT-based approaches were featured in 4 papers, indicating their predominant usage in the field. Additionally, this study presents a novel classification scheme consisting of 10 distinct categories that thoroughly categorize all existing scholarly works on disaster monitoring. However, the study acknowledges limitations related to sycophantic behavior and hallucinations in GPT-based systems and raises ethical considerations and privacy concerns associated with the use of social media data. To address these issues, it proposes strategies for enhancing model robustness, refining data validation techniques, and integrating human oversight mechanisms.