We present MolT5 - a self-supervised learning framework for pretraining models on a vast amount of unlabeled natural language text and molecule strings. MolT5 allows for new, useful, and challenging analogs of traditional vision-language tasks, such as molecule captioning and text-based de novo molecule generation (altogether: translation between molecules and language), which we explore for the first time. Since MolT5 pretrains models on single-modal data, it helps overcome the chemistry domain shortcoming of data scarcity. Furthermore, we consider several metrics, including a new cross-modal embedding-based metric, to evaluate the tasks of molecule captioning and text-based molecule generation. Our results show that MolT5-based models are able to generate outputs, both molecules and captions, which in many cases are high quality.