Multimodal machine translation involves drawing information from more than one modality, based on the assumption that the additional modalities will contain useful alternative views of the input data. The most prominent tasks in this area are spoken language translation, image-guided translation, and video-guided translation, which exploit audio and visual modalities, respectively. These tasks are distinguished from their monolingual counterparts of speech recognition, image captioning, and video captioning by the requirement of models to generate outputs in a different language. This survey reviews the major data resources for these tasks, the evaluation campaigns concentrated around them, the state of the art in end-to-end and pipeline approaches, and also the challenges in performance evaluation. The paper concludes with a discussion of directions for future research in these areas: the need for more expansive and challenging datasets, for targeted evaluations of model performance, and for multimodality in both the input and output space.