Convolutional neural networks can handle an impressive array of supervised learning tasks while relying on a single backbone architecture, suggesting that one solution fits all vision problems. But for many tasks, we can directly make use of the problem structure within neural networks to deliver more accurate predictions. In this thesis, we propose novel deep learning components that exploit the structured output space of an increasingly complex set of problems. We start from Optical Character Recognition (OCR) in natural scenes and leverage the constraints imposed by a spatial outline of letters and language requirements. Conventional OCR systems do not work well in natural scenes due to distortions, blur, or letter variability. We introduce a new attention-based model, equipped with extra information about the neuron positions to guide its focus across characters sequentially. It beats the previous state-of-the-art benchmark by a significant margin. We then turn to dense labeling tasks employing encoder-decoder architectures. We start with an experimental study that documents the drastic impact that decoder design can have on task performance. Rather than optimizing one decoder per task separately, we propose new robust layers for the upsampling of high-dimensional encodings. We show that these better suit the structured per pixel output across the board of all tasks. Finally, we turn to the problem of urban scene understanding. There is an elaborate structure in both the input space (multi-view recordings, aerial and street-view scenes) and the output space (multiple fine-grained attributes for holistic building understanding). We design new models that benefit from a relatively simple cuboidal-like geometry of buildings to create a single unified representation from multiple views. To benchmark our model, we build a new multi-view large-scale dataset of buildings images and fine-grained attributes and show systematic improvements when compared to a broad range of strong CNN-based baselines
