The INTERSPEECH 2020 Computational Paralinguistics Challenge addresses three different problems for the first time in a research competition under well-defined conditions: In the Elderly Emotion Sub-Challenge, arousal and valence in the speech of elderly individuals have to be modelled as a 3-class problem; in the Breathing Sub-Challenge, breathing has to be assessed as a regression problem; and in the Mask Sub-Challenge, speech without and with a surgical mask has to be told apart. 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 partially add deep end-to-end sequential modelling, and, for the first time in the challenge, linguistic analysis.