We consider the problem of multi-task learning, i.e. the setup where there are multiple related prediction problems (tasks), and we seek to improve predictive performance by sharing information across the different tasks. We address this problem using Gaussian process (GP) predictors, using a model that learns a shared covariance function on input-dependent features and a ``free-form'' covariance matrix that specifies inter-task similarity. We discuss the application of the method to a number of real-world problems such as compiler performance prediction and learning robot inverse dynamics. Joint work with Kian Ming Chai, Edwin Bonilla, Stefan Klanke, Sethu Vijayakumar (Edinburgh)