Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference which include the random sweeping and local straining models for isotropic and homogeneous turbulence Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally we summarize the current understanding of space-time correlations and conclude with future issues for the field.