Crises or large-scale emergencies such as earthquakes and hurricanes cause massive damage to lives and property. Crisis response is an essential task to mitigate the impact of a crisis. An effective response to a crisis necessitates information gathering and analysis. Traditionally, this process has been restricted to the information collected by first responders on the ground in the affected region or by official agencies such as local governments involved in the response. However, the ubiquity of mobile devices has empowered people to publish information during a crisis through social media, such as the damage reports from a hurricane. Social media has thus emerged as an important channel of information which can be leveraged to improve crisis response. Twitter is a popular medium which has been employed in recent crises. However, it presents new challenges: the data is noisy and uncurated, and it has high volume and high velocity. In this work, I study four key problems in the use of social media for crisis response: effective monitoring and analysis of high volume crisis tweets, detecting crisis events automatically in streaming data, identifying users who can be followed to effectively monitor crisis, and finally understanding user behavior during crisis to detect tweets inside crisis regions. To address these problems I propose two systems which assist disaster responders or analysts to collaboratively collect tweets related to crisis and analyze it using visual analytics to identify interesting regions, topics, and users involved in disaster response. I present a novel approach to detecting crisis events automatically in noisy, high volume Twitter streams. I also investigate and introduce novel methods to tackle information overload through the identification of information leaders in information diffusion who can be followed for efficient crisis monitoring and identification of messages originating from crisis regions using user behavior analysis.