When a crisis hits, people often turn to social media to ask for help, offer help, find out how others are doing, and decide what they should do. The growth of social media use during crises has been helpful to aid providers as well, giving them a nearly immediate read of the on-the-ground situation that they might not otherwise have. The amount of crisis-related content posted to social media over the past two decades has been explosive, which, in turn, has been a boon to Language Technology (LT) researchers. In this study, we conducted a systematic survey of 355 papers published in the past five years to better understand the expanding growth of LT as it is applied to crisis content, specifically focusing on corpora built over crisis social media data as well as systems and applications that have been developed on this content. We highlight the challenges and possible future directions of research in this space. Our goal is to engender interest in the LT field writ large, in particular in an area of study that can have dramatic impacts on people’s lives. Indeed, the use of LT in crisis response has already been shown to save people’s lives.