Directed evolution and rational design are the two main approaches in protein engineering, which were developed in the quest to solve the limitations of enzymes regarding insufficient catalytic properties. Directed enzyme evolution utilizes random introduction of mutations or focused mutations of the type combinatorial active-site saturation test (CAST)/iterative saturation mutagenesis (ISM), while rational design exploits structural and mechanistic information with computational aids. A panoramic view of directed enzyme evolution and rational enzyme design is given in this chapter, including the methods, aims, and historical developments up to the current status. The relative merits of the approaches are discussed.