In hierarchical cosmologies the evolution of galaxy clustering depends both on cosmological quantities such as Omega, Lambda and P(k), which determine how collapsed structures - dark matter haloes - form and evolve, and on the physical processes - cooling, star formation, radiative and hydrodynamic feedback - which drive the formation of galaxies within these merging haloes. In this paper we combine dissipationless cosmological N-body simulations and semi-analytic models of galaxy formation in order to study how these two aspects interact. We focus on the differences in clustering predicted for galaxies of differing luminosity, colour, morphology and star formation rate, and on what these differences can teach us about the galaxy formation process. We show that a `dip' in the amplitude of galaxy correlations between z=0 and z=1 can be an important diagnostic. Such a dip occurs in low-density CDM models, because structure forms early, and dark matter haloes of mass ~10^12M_solar, containing galaxies with luminosities ~L_*, are unbiased tracers of the dark matter over this redshift range; their clustering amplitude then evolves similarly to that of the dark matter. At higher redshifts, bright galaxies become strongly biased and the clustering amplitude increases again. In high density models, structure forms late, and bias evolves much more rapidly. As a result, the clustering amplitude of L_* galaxies remains constant from z=0 to z=1. The strength of these effects is sensitive to sample selection. The dip becomes weaker for galaxies with lower star formation rates, redder colours, higher luminosities and earlier morphological types. We explain why this is the case, and how it is related to the variation with redshift of the abundance and environment of the observed galaxies. We also show that the relative peculiar velocities of galaxies are biased low in our models, but that this effect is never very strong. Studies of clustering evolution as a function of galaxy properties should place strong constraints on models of galaxy formation and evolution.