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Despite the wide usage of the term, the meaning of this concept is still characterized by great vagueness. A common approach is to evaluate it through self-reports and observational grids. While the former solution suffers from a time-discrepancy problem, since the perceived engagement is evaluated at the end of the interaction, the latter solution may be affected by the subjectivity of the observers. From the perspective of developing socially intelligent robots that autonomously adapt their behaviors during the interaction, replicating the ability to properly detect engagement represents a challenge in the social robotics community. This systematic review investigates the conceptualization of engagement, starting with the works that attempted to automatically detect it in interactions involving robots and real users (i.e., online surveys are excluded). The goal is to describe the most worthwhile research efforts and to outline the commonly adopted definitions (which define the authors\u2019 perspective on the topic) and their connection with the methodology used for the assessment (if any). The research was conducted within two databases (Web of Science and Scopus) between November 2009 and January 2023. A total of 590 articles were found in the initial search. Thanks to an accurate definition of the exclusion criteria, the most relevant papers on automatic engagement detection and assessment in HRI were identified. Finally, 28 papers were fully evaluated and included in this review. The analysis illustrates that the engagement detection task is mostly addressed as a binary or multi-class classification problem, considering user behavioral cues and context-based features extracted from recorded data. One outcome of this review is the identification of current research barriers and future challenges on the topic, which could be clustered in the following fields: engagement components, annotation procedures, engagement features, prediction techniques, and experimental sessions.\n<\/jats:p>","DOI":"10.1007\/s12369-024-01146-w","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T05:01:28Z","timestamp":1717477288000},"page":"1641-1663","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["From the Definition to the Automatic Assessment of Engagement in Human\u2013Robot Interaction: A Systematic Review"],"prefix":"10.1007","volume":"16","author":[{"given":"Alessandra","family":"Sorrentino","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5784-3752","authenticated-orcid":false,"given":"Laura","family":"Fiorini","sequence":"additional","affiliation":[]},{"given":"Filippo","family":"Cavallo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"issue":"4","key":"1146_CR1","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s12369-015-0298-7","volume":"7","author":"SM Anzalone","year":"2015","unstructured":"Anzalone SM, Boucenna S, Ivaldi S, Chetouani M (2015) Evaluating the engagement with social robots. 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