Localizing moments in a longer video via natural language queries is a new, challenging task at the intersection of language and video understanding. Though moment localization with natural language is similar to other language and vision tasks like natural language object retrieval in images, moment localization offers an interesting opportunity to model temporal dependencies and reasoning in text. We propose a new model that explicitly reasons about different temporal segments in a video, and shows that temporal context is important for localizing phrases which include temporal language. To benchmark whether our model, and other recent video localization models, can effectively reason about temporal language, we collect the novel TEMPOral reasoning in video and language (TEMPO) dataset. Our dataset consists of two parts: a dataset with real videos and template sentences (TEMPO - Template Language) which allows for controlled studies on temporal language, and a human language dataset which consists of temporal sentences annotated by humans (TEMPO - Human Language).