A large number of fundamental-mode Love and Rayleigh wave dispersion curves were determined from seismograms for 3330 earthquakes recorded on 258 globally distributed seismographic stations. The dispersion curves were sampled at periods between 25 and 250 s to determine propagation-phase anomalies with respect to a reference earth model. The data set of phase anomalies was first used to construct global isotropic phase-velocity maps at specific frequencies using spherical-spline basis functions with a nominal uniform resolution of 650 km. Azimuthal anisotropy was then included in the parametrization, and its importance for explaining the data explored. Only the addition of 2ζ azimuthal variations for Rayleigh waves was found to be resolved by the data. In the final stage of the analysis, the entire phase-anomaly data set was inverted to determine a global dispersion model for Love and Rayleigh waves parametrized horizontally using a spherical-spline basis, and with a set of B-splines to describe the slowness variations with respect to frequency. The new dispersion model, GDM52, can be used to calculate internally consistent global maps of phase and group velocity, as well as local and path-specific dispersion curves, between 25 and 250 s.