Numerous computer vision problems can be cast as labelling problems where each point of a domain is assigned one of several labels. The case of two labels includes problems like binary segmentation and multiview reconstruction. The case of multiple labels includes problems such as stereo depth reconstruction, image denoising and multi-region segmentation, in particular the piecewise-constant and piecewise smooth Mumford-Shah functional. In my presentation, I will introduce methods of convex relaxation and functional lifting which allow to solve such labelling problems in a spatially continuous setting. Solutions are either globally optimal or within a known bound of the optimum. This is joint work with Kalin Kolev, Maria Klodt, Thomas Pock and Antonin Chambolle.