This thesis presents the research work conducted on developing algo- rithms capable of training neural networks for image classification and re- gression in low supervision settings. The research was conducted on publicly available benchmark image datasets as well as real world data with appli- cations to herbage quality estimation in an agri-tech scope at the VistaMilk SFI centre. Topics include label noise and web-crawled datasets where some images have an incorrect classification label, semi-supervised learning where only a small part of the available images have been annotated by humans and unsupervised learning where the images are not annotated. The principal contributions are summarized as follows. Label noise: a study highlighting the dual in- and out-of-distribution nature of web-noise; a noise detection metric than can independently retrieve each noise type; an observation of the linear separability of in- and out-of-distribution images in unsupervised contrastive feature spaces; two noise-robust algorithms DSOS and SNCF that iteratively improve the state-of-the-art accuracy on the mini-Webvision dataset. Semi-supervised learning: we use unsupervised features to propagate labels from a few labeled examples to the entire dataset; ReLaB an algorithm that allows to decrease the classification error up to 8% with one labeled representative image on CIFAR-10. Biomass composition estimation from images: two semi-supervised approaches that utilize unlabeled images either through an approximate annotator or by adapting semi-supervised algorithms from the image classification litterature. To scale the biomass to drone images, we use super-resolution paired with semi-supervised learning. Early results on grass biomass estimation show the feasibility of automating the process with accuracies on par or better than human experts. The conclusion of the thesis will summarize the research contributions and discuss thoughts on future research that I believe should be tackled in the field of low supervision computer vision.