During disasters, people share their thoughts and emotions on social media and also provide information about the event. Mining the social media messages and updates can be helpful in understanding the emotional state of people during such unforeseen events as they are real-time data. The objective of this review is to explore the feasibility of using social media data for mental health surveillance as well as the techniques used for determining mental health using social media data during disasters. PubMed, PsycINFO, and PsycARTICLES databases were searched from 2009 to November 2018 for primary research studies. After screening and analyzing the records, 18 studies were included in this review. Twitter was the widely researched social media platform for understanding the mental health of people during a disaster. Psychological surveillance was done by identifying the sentiments expressed by people or the emotions they displayed in their social media posts. Classification of sentiments and emotions were done using lexicon-based or machine learning methods. It is not possible to conclude that a particular technique is the best performing one, because the performance of any method depends upon factors such as the disaster size, the volume of data, disaster setting, and the disaster web environment.