A historical perspective of the impact of advanced technologies on compression system design and development for aircraft gas turbine applications is presented. A bright view of the future is projected in which further advancements in compression system technologies will be made. These advancements will have a significant impact on the ability to meet the ever-more-demanding requirements being imposed on the propulsion system for advanced aircraft. Examples are presented of advanced compression system concepts now being studied. The status and potential impact of transitioning from an empirically derived design system to a computationally oriented system are highlighted. A current NASA Lewis Research Center program to enhance this transitioning is described.