Astronomers can now peer far back in time, to redshifts of up toz= 4, and look at galaxies at different stages over 80-90 per cent of the total age of the Universe. A result is that the outline of a consensus about how galaxies form and evolve, as quantified by changes in star-formation rates, is emerging. A hierarchical picture best fits the evidence, one in which small, amorphous proto-galaxies form first, eventually settling into disk galaxies such as spirals, which can then also merge to form ellipticals.