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 report constrained elements covering ~4.2% of the genome. We use evolutionary signatures and comparison with experimental datasets 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 ~1,000 primate- and human-accelerated elements. Overlap with disease-associated variants suggests our findings will be relevant for studies of human biology and health.