We describe the fourth edition of the CheckThat! Lab, part of the 2021 Conference and Labs of the Evaluation Forum (CLEF). The lab evaluates technology supporting tasks related to factuality, and covers Arabic, Bulgarian, English, Spanish, and Turkish. Task 1 asks to predict which posts in a Twitter stream are worth fact-checking, focusing on COVID-19 and politics (in all five languages). Task 2 asks to determine whether a claim in a tweet can be verified using a set of previously fact-checked claims (in Arabic and English). Task 3 asks to predict the veracity of a news article and its topical domain (in English). The evaluation is based on mean average precision or precision at rank k for the ranking tasks, and macro-F1 for the classification tasks. This was the most popular CLEF-2021 lab in terms of team registrations: 132 teams. Nearly one-third of them participated: 15, 5, and 25 teams submitted official runs for tasks 1, 2, and 3, respectively.