The technology development for point-of-care tests (POCTs) targeting respiratory diseases has witnessed a growing demand in the recent past. Investigating the presence of acoustic biomarkers in modalities such as cough, breathing and speech sounds, and using them for building POCTs can offer fast, contactless and inexpensive testing. In view of this, over the past year, we launched the ``Coswara'' project to collect cough, breathing and speech sound recordings via worldwide crowdsourcing. With this data, a call for development of diagnostic tools was announced in the Interspeech 2021 as a special session titled ``Diagnostics of COVID-19 using Acoustics (DiCOVA) Challenge''. The goal was to bring together researchers and practitioners interested in developing acoustics-based COVID-19 POCTs by enabling them to work on the same set of development and test datasets. As part of the challenge, datasets with breathing, cough, and speech sound samples from COVID-19 and non-COVID-19 individuals were released to the participants. The challenge consisted of two tracks. The Track-1 focused only on cough sounds, and participants competed in a leaderboard setting. In Track-2, breathing and speech samples were provided for the participants, without a competitive leaderboard. The challenge attracted 85 plus registrations with 29 final submissions for Track-1. This paper describes the challenge (datasets, tasks, baseline system), and presents a focused summary of the various systems submitted by the participating teams. An analysis of the results from the top four teams showed that a fusion of the scores from these teams yields an area-under-the-curve of 95.1% on the blind test data. By summarizing the lessons learned, we foresee the challenge overview in this paper to help accelerate technology for acoustic-based POCTs.