The comparison of related genomes has emerged as a powerful lens for genome interpretation. Here we report the sequencing and comparative analysis of 29 eutherian genomes. We confirm that at least 5.5% of the human genome has undergone purifying selection, and locate constrained elements covering ∼4.2% of the genome. We use evolutionary signatures and comparisons with experimental data sets to suggest candidate functions for ∼60% of constrained bases. These elements reveal a small number of new coding exons, candidate stop codon readthrough events and over 10,000 regions of overlapping synonymous constraint within protein-coding exons. We find 220 candidate RNA structural families, and nearly a million elements overlapping potential promoter, enhancer and insulator regions. We report specific amino acid residues that have undergone positive selection, 280,000 non-coding elements exapted from mobile elements and more than 1,000 primate- and human-accelerated elements. Overlap with disease-associated variants indicates that our findings will be relevant for studies of human biology, health and disease. This comparative genomics study, comparing the complete human genome sequence with those of 29 placental mammals, including chimpanzees, mice and dogs, identifies 4.2% of the human genome as constrained by evolutionary selection, and ascribes a potential function to about 60% of these constrained bases. A series of evolutionary signatures emerges, providing insights into coding and non-coding functional genomic elements, candidate RNA structural families and aspects of genome organization and evolution. Overlap with disease-associated variants indicates that the findings will be relevant for studies of human disease.