We have used measurements of the expansion history of the Universe H(z), combined with other background tests (CMB shift and SNIa data), to constrain a set of general relativistic dark energy models together with some other models motivated by extra dimensions. Our analysis rests mostly on Bayesian statistics, and we conclude that LCDM is at least substantially favoured, and that braneworld models are less favoured than general relativistic ones. We then look at a new physical parametrisation of dark energy and constrain its parameters with background data. We finally compute cosmological perturbations for a coupled dark energy model finding an instability.