This survey provides an overview of the evolution of visually grounded models of spoken language over the last 20 years. Such models are inspired by the observation that when children pick up a language, they rely on a wide range of indirect and noisy clues, crucially including signals from the visual modality co-occurring with spoken utterances. Several fields have made important contributions to this approach to modeling or mimicking the process of learning language: Machine Learning, Natural Language and Speech Processing, Computer Vision and Cognitive Science. The current paper brings together these contributions in order to provide a useful introduction and overview for practitioners in all these areas. We discuss the central research questions addressed, the timeline of developments, and the datasets which enabled much of this work. We then summarize the main modeling architectures and offer an exhaustive overview of the evaluation metrics and analysis techniques.