The INTERSPEECH 2021 Computational Paralinguistics Challenge addresses four different problems for the first time in a research competition under well-defined conditions: In the COVID-19 Cough and COVID-19 Speech Sub-Challenges, a binary classification on COVID-19 infection has to be made based on coughing sounds and speech; in the Escalation Sub- Challenge, a three-way assessment of the level of escalation in a dialogue is featured; and in the Primates Sub-Challenge, four species vs background need to be classified. We describe the Sub-Challenges, baseline feature extraction, and classifiers based on the 'usual' COMPARE and BoAW features as well as deep unsupervised representation learning using the AUDEEP toolkit, and deep feature extraction from pre-trained CNNs using the DEEP SPECTRUM toolkit; in addition, we add deep end-to-end sequential modelling, and partially linguistic analysis.