Extracting information from text entails deriving a structured, and typically domain-specific, representation of entities and relations from unstructured text. The information thus extracted can potentially facilitate applications such as question answering, information retrieval, conversational dialogue and opinion analysis. However, extracting information from text in a structured form is difficult: it requires understanding words and the relations that exist between them in the context of both the current sentence and the document as a whole. In this thesis, we present our research on neural models that learn structured output representations comprised of textual mentions of entities and relations within a sentence. In particular, we propose the use of novel output representations that allow the neural models to learn better dependencies in the output structure and achieve state-of-the-art performance on both tasks. We also propose models which can learn nested variation of the problem of entity mentions and achieves state-of-the-art performance. We also present our recent work on expanding the input context beyond sentences by incorporating coreference resolution to learn entity-level rather than mention-level representations and show that these representations are important for improving relation extraction. We perform analysis to show that the entity-level representations which capture the information regarding the saliency of entities in the document are beneficial for relation extraction. We also briefly mention about incorporating biases into the neural network models and show improvements in the performance of information extraction.