We describe a method to invert surface wave dispersion data for a model of shear velocities with uncertainties in the crust and uppermost mantle. The inversion is a multistep process, constrained by a priori information, that culminates in a Markov-chain Monte-Carlo sampling of model space to yield an ensemble of acceptable models at each spatial node. The model is radially anisotropic in the uppermost mantle to an average depth of about 200 km and is isotropic elsewhere. The method is applied on a 2°× 2° grid globally to a large data set of fundamental mode surface wave group and phase velocities (Rayleigh group velocity, 16–200 s; Love group velocity, 16–150 s; Rayleigh and Love phase velocity, 40–150 s). The middle of the ensemble (Median Model) defines the estimated model and the half-width of the corridor of models provides the uncertainty estimate. Uncertainty estimates allow the identification of the robust features of the model which, typically, persist only to depths of ∼250 km. We refer to the features that appear in every member of the ensemble of acceptable models as ‘persistent’. Persistent features include sharper images of the variation of oceanic lithosphere and asthenosphere with age, continental roots, extensional tectonic features in the upper mantle, the shallow parts of subducted lithosphere, and improved resolution of radial anisotropy. In particular, we find no compelling evidence for ‘negative anisotropy’ anywhere in the world's lithosphere.