According to the paradigm of hierarchical clustering, deviant motions from cosmic expansion arise as matter segregates into high and low regimes. It is possible to determine, alternatively, the motions that should arise from the observed distribution of galaxies or the distribution of matter from the observed motions of galaxies. It is a fundamental success of the paradigm that the two methodologies are in general agreement.

In recent years there has been significant improvement in our knowledge of both the distribution of galaxies through comprehensive redshift surveys and the deviant motions of galaxies through measurements of distances. These observational advances have stimulated interest in methods of interpretation. The constraints on the distribution of matter and cosmological parameters are becoming increasingly precise. Yet major questions remain.