We present an overview of Task 1 of the fourth edition of the CheckThat! Lab, part of the 2021 Conference and Labs of the Evaluation Forum (CLEF). The task asks to predict which posts in a Twitter stream are worth fact-checking, focusing on COVID-19 and politics in five languages: Arabic, Bulgarian, English, Spanish, and Turkish. A total of 15 teams participated in this task and most submissions managed to achieve sizable improvements over the baselines using Transformer-based models such as BERT and RoBERTa. Here, we describe the process of data collection and the task setup, including the evaluation measures, and we give a brief overview of the participating systems. We release to the research community all datasets from the lab as well as the evaluation scripts, which should enable further research in check-worthiness estimation for tweets and political debates. © 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).