The expansion of the Universe can be retarded in localised regions within the Universe both by the presence of gravity and by non-gravitational motions generated in the post-recombination Universe. The motions of galaxies thus generated are called 'peculiar motions', and the amplitudes, size scales and coherence of these peculiar motions are among the most direct records of the structure of the Universe. As such, measurements of these properties of the present-day Universe provide some of the severest tests of cosmological theories. The author presents a review of the evidence for large-scale motions of galaxies out to a distance of approximately 5000 km s-1.