The present invention relates to systems which harness the molecular biology of a living cell to direct evolution of biological entities of interest. According to the invention, a host cell is engineered to facilitate mutation of a nucleic acid target corresponding to that entity and select for desirable mutants. As applied to populations of host cells, the invention provides a means to generate and contemporaneously select mutants of interest, allowing for the production of extremely diverse libraries enriched in the most "fit" mutants.