One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform it is possible to establish dependencies between output variables. Two important aspects in this framework are how can we introduce prior knowledge and how can we perform efficient inference. Relating the convolution operation with dynamical systems, we can specify richer covariance functions for multiple outputs. We also present different sparse approximations for dependent output Gaussian processes in the context of structured covariances. Joint work with Neil Lawrence, David Luengo and Michalis Titsias.