This talk will discuss a newly introduced family of Bayesian approaches aiming at combining the structural advantages of deep models with the expressive power of Gaussian processes. The resulting algorithms could find potential applications in many domains, such as vision, robotics and bioinformatics. The backbone of the methods is a hierarchy of layers of latent variables, with Gaussian processes governing the mappings between the layers. The first part of the talk will focus only on a two-layer architecture, as this is an interesting model on its own: it can be seen as a powerful warping framework that allows for non-linearly transforming the GP inputs. This will be demonstrated in high-dimensional dynamical (e.g. video) data. In another extension, it will be shown how the integrated Bayesian mechanism allows for softly segmenting the learned feature space automatically into private / shared parts when the observed data come in different views, for example silhouette / motion capture pairs. In the second part of the talk, it will be demonstrated how more abstract learning can be achieved with deeper hierarchies, focusing on the case where data are scarce.