We use recent progress in simulating the production of magnetohydrodynamic jets around black holes to derive the cosmic spin history of the most massive black holes. Our work focusses on black holes with masses ∼> 108 M⊙. Under the assumption that the efficiency of jet production is a function of spin ˆa, as given by the simulations, we can approximately reproduce the observed ‘radio loudness’ of quasars and the local radio luminosity function.Using the X-ray luminosity function and the local mass function of supermassive black holes, SMBHs, we can reproduce the individual radio luminosity functions of radio sources showing high- and low-excitation narrow emission lines. We find that the data favour spin distributions that are bimodal, with one component around spin zero and the other close to maximal spin. The ‘typical’ spin is therefore really the expectation value, lying between the two peaks. In the low-excitation galaxies, the two components have similar amplitudes, meaning approximately half of the sources have very high spins, and the other have very low spins. For the high-excitation galaxies, the amplitude of the high-spin peak is typically much smaller than that of the low-spin peak, so that most of the sources have low spins. However, a small population of near maximally spinning high-accretion rate objects is inferred. A bimodality should be seen in the radio loudness of quasars, although there are a variety of physical and selection effects that may obfuscate this feature. We predict that the low-excitation galaxies are dominated by SMBHs with masses ∼> 108 M⊙, down to radio luminosity densities ∼1021 W Hz−1 sr−1 at 1.4 GHz. Under reasonable assumptions, our model is also able to predict the radio luminosity function at z=1, and predicts it to be dominated by radio sources with high-excitation narrow emission lines above luminosity densities ∼> 1026 W Hz−1 sr−1 at 1.4 GHz, and this is in full agreement with the observations. From our parametrisation of the spin distributions of the high- and low-accretion rate SMBHs, we derive an estimate of the spin history of SMBHs, which shows a weak evolution between z=1 and 0. A larger fraction of low-redshift SMBHs have high spins compared to high-redshift SMBHs. Using the best fitting jet efficiencies there is marginal evidence for evolution in spin: the mean spin increases slightly from hˆai∼0.25 at z=1 to hˆai∼0.35 at z=0, and the fraction of SMBHs with ˆa>0.5 increases from 0.16±0.03 at z=1 to 0.24±0.09 at z=0. Our inferred spin history of SMBHs is in excellent agreement with constraints from the mean radiative efficiency of quasars, as well as the results from recent simulations of growing SMBHs. We discuss the implications in terms of accretion and SMBH mergers. We also discuss other work related to the spin of SMBHs as well as work discussing the spin of galactic black holes and their jet powers.