Abstract. Messages on social media can be an important source of information during crisis situations. They can frequently provide details about developments much faster than traditional sources (e.g., official news) and can offer personal perspectives on events, such as opinions or specific needs. In the future, these messages can also serve to assess disaster risks. One challenge for utilizing social media in crisis situations is the reliable detection of relevant messages in a flood of data. Researchers have started to look into this problem in recent years, beginning with crowdsourced methods. Lately, approaches have shifted towards an automatic analysis of messages. A major stumbling block here is the question of exactly what messages are considered relevant or informative, as this is dependent on the specific usage scenario and the role of the user in this scenario. In this review article, we present methods for the automatic detection of crisis-related messages (tweets) on Twitter. We start by showing the varying definitions of importance and relevance relating to disasters, leading into the concept of use case-dependent actionability that has recently become more popular and is the focal point of the review paper. This is followed by an overview of existing crisis-related social media data sets for evaluation and training purposes. We then compare approaches for solving the detection problem based (1) on filtering by characteristics like keywords and location, (2) on crowdsourcing, and (3) on machine learning technique. We analyze their suitability and limitations of the approaches with regards to actionability. We then point out particular challenges, such as the linguistic issues concerning social media data. Finally, we suggest future avenues of research and show connections to related tasks, such as the subsequent semantic classification of tweets.