In this paper, we introduce Iterative Text Summarization (ITS), an iteration-based model for supervised extractive text summarization, inspired by the observation that it is often necessary for a human to read an article multiple times in order to fully understand and summarize its contents. Current summarization approaches read through a document only once to generate a document representation, resulting in a sub-optimal representation. To address this issue we introduce a model which iteratively polishes the document representation on many passes through the document. As part of our model, we also introduce a selective reading mechanism that decides more accurately the extent to which each sentence in the model should be updated. Experimental results on the CNN/DailyMail and DUC2002 datasets demonstrate that our model significantly outperforms state-of-the-art extractive systems when evaluated by machines and by humans.