The invention relates to methods of producing eukaryotic cell libraries encoding a repertoire of binding molecules ("binders"), wherein the methods use a site-specific nuclease for targeted cleavage of cellular DNA to enhance integration of binder genes through endogenous cellular repair mechanisms. Populations of eukaryotic cells are produced in which a repertoire of genes encoding binders are integrated into a desired locus in cellular DNA (e.g., a genomic locus) allowing expression of the encoded binding molecule, thereby creating a population of cells expressing different binders.