Social media (e.g., Twitter and Facebook) can be regarded as vital sources of information during disasters to improve situational awareness (SA) and disaster management since they play a significant role in the rapid spread of information in the event of a disaster. Due to the volume of data is far beyond the capabilities of manual examination, existing works utilize natural language processing methods based on keywords, or classification models relying on features derived from text and other metadata (e.g., user profiles) to extract social media data contributing to SA and automatically categorize them into the relevant classes (e.g., damage and donation). However, the design of the classification schema and the associated information extraction methods are far less than straightforward and highly depend on: (1) the event type, (2) the study or analysis purpose, and (3) the social media platform used. To this end, this paper reviews the literature for extracting social media data and provides an overview of classification schemas that have been used to assess SA in events involving natural hazards from five different analytical perspectives (content, temporal, user, sentiment, and spatiotemporal) by discussing the prevalent topic categories, disaster event types, purpose of studies, and platforms utilized from each schema. Finally, this paper summarizes classification methods, and platforms that are most commonly used for each disaster event type, and outlines a research agenda with recommendations for future innovations.