Rich entity representations are useful for a wide class of problems involving entities. Despite their importance, there is no standardized benchmark that evaluates the overall quality of entity representations. In this work, we propose EntEval: a test suite of diverse tasks that require nontrivial understanding of entities including entity typing, entity similarity, entity relation prediction, and entity disambiguation. In addition, we develop training techniques for learning better entity representations by using natural hyperlink annotations in Wikipedia. We identify effective objectives for incorporating the contextual information in hyperlinks into state-of-the-art pretrained language models and show that they improve strong baselines on multiple EntEval tasks.