Disasters have long been a scourge for humanity. With the advances in technology (in terms of computing, communications, and the ability to process, and analyze big data), our ability to respond to disasters is at an inflection point. There is great optimism that big data tools can be leveraged to process large amounts of crisis-related data (in the form of user generated data in addition to traditional humanitarian data) to provide an insight into the fast-changing situation and help drive an effective disaster response. This article introduces the history and the future of big crisis data analytics, along with a discussion on its promise, enabling technologies, challenges, and pitfalls.