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Critiquing-based recommender systems elicit users' feedback, called critiques, which they made on the recommended items. This conversational style of interaction is in contract to the standard model where users receive recommendations in a single interaction. Through the use of the critiquing feedback, the recommender systems are able to more accurately learn the users' profiles, and therefore suggest better recommendations in the subsequent rounds. Critiquing-based recommenders have been widely studied in knowledge-, content-, and preference-based recommenders and are beginning to be tried in several online websites, such as MovieLens. This article examines the motivation and development of the subject area, and offers a detailed survey of the state of the art concerning the design of critiquing interfaces and development of algorithms for critiquing generation. With the help of categorization analysis, the survey reveals three principal branches of critiquing based recommender systems, using respectively natural language based, system-suggested, and user-initiated critiques. Representative example systems will be presented and analyzed for each branch, and their respective pros and cons will be discussed. Subsequently, a hybrid framework is developed to unify the advantages of different methods and overcome their respective limitations. Empirical findings from user studies are further presented, indicating how hybrid critiquing supports could effectively enable end-users to achieve more confident decisions. Finally, the article will point out several future trends to boost the advance of critiquing-based recommenders.