This thesis presents the work done in the area of semi-supervised learning, label noise, and budgeted training for deep learning approaches to computer vision. The improvements seen in computer vision since the successful introduction of deep learning rely on the availability of large amounts of labeled data and long lasting training processes. First, this research studies the three main alternatives to fully supervised deep learning categorized in three different levels of supervision: unsupervised learning (no label involved), semi-supervised learning (a small set of labeled data is available), and label noise (all the samples are labeled but some of them are incorrect). These alternatives aim at reducing the cost of building fully annotated and finely curated datasets, which in most cases is time consuming and requires expert annotators. State-of-the-art performance has been achieved in several semi-supervised, unsupervised, and label noise benchmarks including CIFAR10, CIFAR100, and STL-10. Additionally, the solutions proposed for learning in the presence of label noise have been validated in realistic benchmarks built with datasets annotated from web information: WebVision and Clothing1M. Second, this research explores alternatives to reduce the computational cost of the training of deep learning systems that currently require hours or days to reach state-of-the-art performance. Particularly, this research studied budgeted training, i.e.~when the training process is limited to a fixed number of iterations. Experiments in this setup showed that for better model convergence, variety in the data is preferable than the importance of the samples used during training. As a result of this research, three main author publications have been generated, one more has been recently submitted to review for a conference, and several other secondary author publications have been produced in close collaboration with other researchers in the centre.