A fundamental limitation of standard machine learning methods is the cost incurred by the preparation of the large training samples required for good generalization. A potential remedy is offered by multi-task learning: in many cases, while individual sample sizes are rather small, there are samples to represent a large number of learning tasks (linear regression problems), which share some constraining or generative property. If this property is suficiently simple it should allow for better learning of the individual tasks despite their small individual sample sizes. In this talk I will review a wide class of multi-task learning methods which encourage low-dimensional representations of the regression vectors. I will describe techniques to solve the underlying optimization problems and present an analysis of the generalization performance of these learning methods which provides a proof of the superiority of multi-task learning under specific conditions.