Evolutionary genomics identifies multiple constraints that differentially affect different parts of the genomes of diverse life forms. The selective pressures that shape the evolution of viral, prokaryotic, and eukaryotic genomes differ dramatically, and substantial differences exist even between animal and bacterial lineages. Constraints on protein evolution appear to be more universal and could be determined by the fundamental physics of protein folding. Some key features of the molecular phenome such as protein abundance turn out to be unexpectedly conserved and hence strongly constrained. The constraints that shape the evolution of genomes and phenomes are complemented by the plasticity and robustness of genome architecture, expression, and regulation. Several universal “laws” of genome and phenome evolution were detected, some of which seem to be dictated by selective constraints and others by neutral process.