The objectives of this work are cross-modal text-audio and audio-text retrieval, in which the goal is to retrieve the audio content from a pool of candidates that best matches a given written description and vice versa. Text-audio retrieval enables users to search large databases through an intuitive interface: they simply issue free-form natural language descriptions of the sound they would like to hear. To study the tasks of text-audio and audio-text retrieval, which have received limited attention in the existing literature, we introduce three challenging new benchmarks. We first construct text-audio and audio-text retrieval benchmarks from the AudioCaps and Clotho audio captioning datasets. Additionally, we introduce the SoundDescs benchmark, which consists of paired audio and natural language descriptions for a diverse collection of sounds that are complementary to those found in AudioCaps and Clotho. We employ these three benchmarks to establish baselines for cross-modal text-audio and audio-text retrieval, where we demonstrate the benefits of pre-training on diverse audio tasks. We hope that our benchmarks will inspire further research into audio retrieval with free-form text queries. Code, audio features for all datasets used, and the SoundDescs dataset are publicly available at https://github.com/akoepke/audio-retrieval-benchmark.