Computer audition (CA) has been demonstrated to be efficient in healthcare domains for speech-affecting disorders (e.g., autism spectrum, depression, or Parkinson's disease) and body sound-affecting abnormalities (e. g., abnormal bowel sounds, heart murmurs, or snore sounds). Nevertheless, CA has been underestimated in the considered data-driven technologies for fighting the COVID-19 pandemic caused by the SARS-CoV-2 coronavirus. In this light, summarise the most recent advances in CA for COVID-19 speech and/or sound analysis. While the milestones achieved are encouraging, there are yet not any solid conclusions that can be made. This comes mostly, as data is still sparse, often not sufficiently validated and lacking in systematic comparison with related diseases that affect the respiratory system. In particular, CA-based methods cannot be a standalone screening tool for SARS-CoV-2. We hope this brief overview can provide a good guidance and attract more attention from a broader artificial intelligence community.