Vision-and-language research consists of a diverse set of tasks. While underlying image datasets, input/output APIs, and model architectures vary across tasks, there exists a common need to associate imagery and text -- i.e. to perform visual grounding. Despite this, the standard paradigm has been to treat each task in isolation -- starting from separately pretrained vision and language models and then learning to associate their outputs as part of task training. This siloed approach fails to leverage grounding supervision between tasks and can result in myopic groundings when datasets are small or biased. In this talk, I'll discuss a line of work focused on learning task-agnostic visiolinguistic representations that can serve as a common foundation for many vision-and-language tasks. First, I'll cover recent work on learning a generic multimodal encoder from large-scale web data and transferring this pretrained model to a range of vision-and-language tasks. Second, I'll show how multitask training from this base architecture further improves task performance while unifying twelve vision-and-language tasks in a single model.