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Most general-purpose extractive summarization models are trained on news articles, which are short and present all important information upfront. As a result, such models are biased on position and often perform a smart selection of sentences from the beginning of the document. When summarizing long narratives, which have complex structure and present information piecemeal, simple position heuristics are not sufficient. In this paper, we propose to explicitly incorporate the underlying structure of narratives into general unsupervised and supervised extractive summarization models. We formalize narrative structure in terms of key narrative events (turning points) and treat it as latent in order to summarize screenplays (i.e., extract an optimal sequence of scenes). Experimental results on the CSI corpus of TV screenplays, which we augment with scene-level summarization labels, show that latent turning points correlate with important aspects of a CSI episode and improve summarization performance over general extractive algorithms leading to more complete and diverse summaries.