What audio embedding approach generalizes best to a wide range of downstream tasks across a variety of everyday domains without fine-tuning? The aim of the HEAR benchmark is to develop a general-purpose audio representation that provides a strong basis for learning in a wide variety of tasks and scenarios. HEAR evaluates audio representations using a benchmark suite across a variety of domains, including speech, environmental sound, and music. HEAR was launched as a NeurIPS 2021 shared challenge. In the spirit of shared exchange, each participant submitted an audio embedding model following a common API that is general-purpose, open-source, and freely available to use. Twenty-nine models by thirteen external teams were evaluated on nineteen diverse downstream tasks derived from sixteen datasets. Open evaluation code, submitted models and datasets are key contributions, enabling comprehensive and reproducible evaluation, as well as previously impossible longitudinal studies. It still remains an open question whether one single general-purpose audio representation can perform as holistically as the human ear.