Understanding human language often necessitates understanding entities and their place in a taxonomy of knowledge -- their types. Previous methods to learn entity types rely on training classifiers on datasets with coarse, noisy, and incomplete labels. We introduce a method to instill fine-grained type knowledge in language models with text-to-text pre-training on type-centric questions leveraging knowledge base documents and knowledge graphs. We create the WikiWiki dataset: entities and passages from 10M Wikipedia articles linked to the Wikidata knowledge graph with 41K types. Models trained on WikiWiki achieve state-of-the-art performance in zero-shot dialog state tracking benchmarks, accurately infer entity types in Wikipedia articles, and can discover new types deemed useful by human judges.