Direct observations of the Hubble rate, from cosmic chronometers and the radial baryon acoustic oscillation scale, can outperform supernovae observations in understanding the expansion history, because supernovae observations need to be differentiated to extract H(z). We use existing H(z) data and smooth the data using a new Gaussian processes package, GaPP, from which we can also estimate derivatives. The obtained Hubble rate and its derivatives are used to reconstruct the equation of state of dark energy and to perform consistency tests of the ΛCDM model, some of which are newly devised here. Current data are consistent with the concordance model, but are rather sparse. Future observations will provide a dramatic improvement in our ability to constrain or refute the concordance model of cosmology. We produce simulated data to illustrate how effective H(z) data will be in combination with Gaussian processes.