We present the GermEval 2021 shared task on the identification of toxic, engaging, and fact-claiming comments. This shared task comprises three binary classification subtasks with the goal to identify: toxic comments, engaging comments, and comments that include indications of a need for fact-checking, here referred to as fact-claiming comments. Building on the two previous GermEval shared tasks on the identification of offensive language in 2018 and 2019, we extend this year's task definition to meet the demand of moderators and community managers to also highlight comments that foster respectful communication, encourage in-depth discussions, and check facts that lines of arguments rely on. The dataset comprises 4,188 posts extracted from the Facebook page of a German political talk show of a national public television broadcaster. A theoretical framework and additional reliability tests during the data annotation process ensure particularly high data quality. The shared task had 15 participating teams submitting 31 runs for the subtask on toxic comments, 25 runs for the subtask on engaging comments, and 31 for the subtask on fact-claiming comments. The shared task website can be found at https://germeval2021toxic.github.io/SharedTask/.