We describe the third edition of the CheckThat! Lab, which is part of the 2020 Cross-Language Evaluation Forum (CLEF). CheckThat! proposes four complementary tasks and a related task from previous lab editions, offered in English, Arabic, and Spanish. Task 1 asks to predict which tweets in a Twitter stream are worth fact-checking. Task 2 asks to determine whether a claim posted in a tweet can be verified using a set of previously fact-checked claims. Task 3 asks to retrieve text snippets from a given set of Web pages that would be useful for verifying a target tweet’s claim. Task 4 asks to predict the veracity of a target tweet’s claim using a set of potentially-relevant Web pages. Finally, the lab offers a fifth task that asks to predict the check-worthiness of the claims made in English political debates and speeches. CheckThat! features a full evaluation framework. The evaluation is carried out using mean average precision or precision at rank k for ranking tasks, and F1 for classification tasks.