An individual passes on random segments of her genome to future generations: typically, most of the genome is lost, but a small fraction survives, in many copies. This distribution of surviving blocks can be calculated using a branching process argument. Remarkably, after a few tens of generations it has the same form for every individual, with variation in reproductive value between individuals only affecting the probability of survival. These results follow the descent of genomes forwards in time. The converse problem is to ask how far back we can reconstruct the pedigree, given a sample of complete genomes.