The success of a disaster relief and response process is largely dependent on timely and accurate information regarding the status of the disaster, the surrounding environment, and the affected people. This information is primarily provided by first responders on-site and can be enhanced by the firsthand reports posted in real-time on social media. Many tools and methods have been developed to automate disaster relief by extracting, analyzing, and visualizing actionable information from social media. However, these methods are not well integrated in the relief and response processes and the relation between the two requires exposition for further advancement. In this survey, we review the new frontier of intelligent disaster relief and response using social media, show stages of disasters which are reflected on social media, establish a connection between proposed methods based on social media and relief efforts by first responders, and outline pressing challenges and future research directions.