In the era of technological advancement, social media has emerged as a vital player in disaster management. It facilitates the dis-semination of information by both responders and victims, offering a direct channel for communication with authorities—a feature notably absent in traditional media. The diversity of languages, including regional ones, introduces complexity in comprehending and extracting valuable insights from text-based social media data. Recent progress in Natural Language Processing (NLP), coupled with Machine Learning (ML) and Deep Learning (DL), has been applied to address the challenges presented by disasters on social media. This paper conducts a thorough review of NLP-based research studies focused on social media data related to natural disaster management, particularly those conducted since 2016. The paper delves into the findings and concludes with reflections and suggestions for future research in this field.