The recent breakthroughs in machine learning (ML) and deep learning (DL) have enabled many new capabilities across plenty of application domains. While most existing machine learning models require large memory and computing power, efforts have been made to deploy some models on resource-constrained devices as well. There are several systems that perform inference on the device, while direct training on the device still remains a challenge. On-device training, however, is attracting more and more interest because: (1) it enables training models on local data without needing to share data over the cloud, thus enabling privacy preserving computation by design; (2) models can be refined on devices to provide personalized services and cope with model drift in order to adapt to the changes of the real-world environment; and (3) it enables the deployment of models in remote, hardly accessible locations or places without stable internet connectivity. We summarize and analyze the-state-of-art systems research to provide the first survey of on-device training from a systems perspective.