To advance understanding on how to engage readers, we advocate the novel task of automatic pull quote selection. Pull quotes are a component of articles specifically designed to catch the attention of readers with spans of text selected from the article and given more salient presentation. This task differs from related tasks such as summarization and clickbait identification by several aspects. We establish a spectrum of baseline approaches to the task, ranging from handcrafted features to a neural mixture-of-experts to cross-task models. By examining the contributions of individual features and embedding dimensions from these models, we uncover unexpected properties of pull quotes to help answer the important question of what engages readers. Human evaluation also supports the uniqueness of this task and the suitability of our selection models. The benefits of exploring this problem further are clear: pull quotes increase enjoyment and readability, shape reader perceptions, and facilitate learning. Code to reproduce this work is available at https://github.com/tannerbohn/AutomaticPullQuoteSelection.