Galaxies as a cosmological test

The relativistic LambdaCDM cosmological model has passed a demanding network of tests that convincingly demonstrate it is a useful approximation to what happened back to high redshift. But there are anomalies in its application to structure formation on the scales of galaxies that show we have much to learn about what this theory actually predicts and possibly something also of value to learn about the fundamental theoretical basis for observational cosmology. This is slightly revised and enlarged from a contribution to A Century of Cosmology, Venice, August 2007.