COVID-19 heavily affects breathing and voice and causes symptoms that make patients’ voices distinctive, creating recognizable audio signatures. Initial studies have already suggested the potential of using voice as a screening solution. In this article we present a dataset of voice, cough and breathing audio recordings collected from individuals infected by SARS-CoV-2 virus, as well as non-infected subjects via large scale crowdsourced campaign. We describe preliminary results for detection of COVID-19 from cough patterns using standard acoustic features sets, wavelet scattering features and deep audio embeddings extracted from low-level feature representations (VGGish and OpenL3). Our models achieve accuracy of 88.52%, sensitivity of 88.75% and specificity of 90.87%, confirming the applicability of audio signatures to identify COVID-19 symptoms. We furthermore provide an in-depth analysis of the most informative acoustic features and try to elucidate the mechanisms that alter the acoustic characteristics of coughs of people with COVID-19.