In recent years, advances in speech recognition and machine translation (MT) have led to wide adoption, for example, helping people issue voice commands to their phones and talk with people who do not speak the same language. These advances are made possible by the use of neural network methods on large, high-quality datasets. However, computers still struggle to understand the meaning of natural language. In this talk, I will present two efforts to scale up natural language understanding, drawing inspiration from recent successes in speech and MT. First, I will discuss conversational agents that are learned from scratch in a purely data-driven way, by adapting techniques from statistical machine translation. In the second part of the talk, I will describe an effort to extract structured knowledge from text, without relying on slow and expensive human labeling. Our approach combines the benefits of structured learning and neural networks and accurately predicts sentence-level relation mentions given only indirect supervision from a knowledge base. By explicitly reasoning about missing data during learning, this method enables large-scale training of convolutional neural networks while mitigating the issue of label noise inherent in distant supervision. Our method achieves state-of-the-art results on minimally supervised sentence-level relation extraction, outperforming several baselines, including a competitive approach that uses the attention layer of a purely neural model.