In-vitro display technologies combine two important advantages for identifying and optimizing ligands by evolutionary strategies. First, by obviating the need to transform cells in order to generate and select libraries, they allow a much higher library diversity. Second, by including PCR as an integral step in the procedure, they make PCR-based mutagenesis strategies convenient. The resulting iteration between diversification and selection allows true Darwinian protein evolution to occur in vitro. We describe two such selection methods, ribosome display and mRNA display. In ribosome display, the translated protein remains connected to the ribosome and to its encoding mRNA; the resulting ternary complex is used for selection. In mRNA display, mRNA is first translated and then covalently bonded to the protein it encodes, using puromycin as an adaptor molecule. The covalent mRNA-protein adduct is purified from the ribosome and used for selection. Successful examples of high-affinity, specific target-binding molecules selected by in-vitro display methods include peptides, antibodies, enzymes, and engineered scaffolds, such as fibronectin type III domains and synthetic ankyrins, which can mimic antibody function.