The present invention provides molecules, including IgGs, non-IgG immunoglobulin, proteins and non-protein agents, that have increased in vivo half-lives due to the presence of an IgG constant domain, or a portion thereof that binds the FcRn, having one or more amino acid modifications that increase the affinity of the constant domain or fragment for FcRn. Such proteins and molecules with increased half-lives have the advantage that smaller amounts and or less frequent dosing is required in the therapeutic, prophylactic or diagnostic use of such molecules.