Controllable summarization aims to provide summaries that take into account user-specified aspects and preferences to better assist them with their information need, as opposed to the standard summarization setup which build a single generic summary of a document. We introduce a human-annotated data set EntSUM for controllable summarization with a focus on named entities as the aspects to control. We conduct an extensive quantitative analysis to motivate the task of entity-centric summarization and show that existing methods for controllable summarization fail to generate entity-centric summaries. We propose extensions to state-of-the-art summarization approaches that achieve substantially better results on our data set. Our analysis and results show the challenging nature of this task and of the proposed data set.