Opinion mining from customer reviews has become pervasive in recent years. Sentences in reviews, however, are usually classified independently, even though they form part of a review's argumentative structure. Intuitively, sentences in a review build and elaborate upon each other; knowledge of the review structure and sentential context should thus inform the classification of each sentence. We demonstrate this hypothesis for the task of aspect-based sentiment analysis by modeling the interdependencies of sentences in a review with a hierarchical bidirectional LSTM. We show that the hierarchical model outperforms two non-hierarchical baselines, obtains results competitive with the state-of-the-art, and outperforms the state-of-the-art on five multilingual, multi-domain datasets without any hand-engineered features or external resources.