Despite more than 50 years of investigation, it is still unclear how the underlying structure of relaxor ferroelectrics gives rise to their defining properties, such as ultrahigh piezoelectric coefficients, high permittivity over a broad temperature range, diffuse phase transitions, strong frequency dependence in dielectric response, and phonon anomalies1,2,3,4,5,6,7,8,9,10. The model of polar nanoregions inside a non-polar matrix has been widely used to describe the structure of relaxor ferroelectrics11. However, the lack of precise knowledge about the shapes, growth and dipole patterns of polar nanoregions has led to the characterization of relaxors as “hopeless messes”12, and no predictive model for relaxor behaviour is currently available. Here we use molecular dynamics simulations of the prototypical Pb(Mg 1/3 ,Nb 2/3 )O 3 –PbTiO 3 relaxor material to examine its structure and the spatial and temporal polarization correlations. Our simulations show that the unusual properties of relaxors stem from the presence of a multi-domain state with extremely small domain sizes (2–10 nanometres), and no non-polar matrix, owing to the local dynamics. We find that polar structures in the multi-domain state in relaxors are analogous to those of the slush state of water. The multi-domain structure of relaxors that is revealed by our molecular dynamics simulations is consistent with recent experimental diffuse scattering results and indicates that relaxors have a high density of low-angle domain walls. This insight explains the recently discovered classes of relaxors13 that cannot be described by the polar nanoregion model, and provides guidance for the design and synthesis of new relaxor materials.