Social media platforms provide active communication channels during mass convergence and emergency events such as disasters caused by natural hazards. As a result, first responders, decision makers, and the public can use this information to gain insight into the situation as it unfolds. In particular, many social media messages communicated during emergencies convey timely, actionable information. Processing social media messages to obtain such information, however, involves solving multiple challenges including: handling information overload, filtering credible information, and prioritizing different classes of messages. These challenges can be mapped to classical information processing operations such as filtering, classifying, ranking, aggregating, extracting, and summarizing. We survey the state of the art regarding computational methods to process social media messages, focusing on their application in emergency response scenarios. We examine the particularities of this setting, and then methodically examine a series of key sub-problems ranging from the detection of events to the creation of actionable and useful summaries.