We present a survey covering the state of the art in low-resource machine translation (MT) research. There are currently around 7,000 languages spoken in the world and almost all language pairs lack significant resources for training machine translation models. There has been increasing interest in research addressing the challenge of producing useful translation models when very little translated training data is available. We present a summary of this topical research field and provide a description of the techniques evaluated by researchers in several recent shared tasks in low-resource MT.