Enzymes are extremely efficient natural catalysts of a variety of chemical reactions. Design of enzymes with new functions and properties has become one of the main goals of modern protein engineering. The field of protein engineering is growing intensively, and different strategies were developed for the creation of enzymes with new properties. While there is plenty of methods and instruments, all modern protein engineering strategies could be divided in two major groups, broadly based on the core ideas of rational design or directed evolution. DNA-dependent proteins present an important target of protein engineering due to their wide use in molecular cloning, bioanalytics, and genetic manipulations. Here we review examples of successful application of biochemical, structural and computational approaches belonging to both protein engineering strategies to create new proteins belonging to three important classes of DNA-dependent enzymes: CRISPR-associated nuclease Cas9, DNA polymerases, and DNA glycosylases. The review contains examples of successfully designed enzymes and discusses the most useful approaches in the engineering of these specific enzyme classes, problems restraining the development of this field, and future directions in the development and application of designed DNA-dependent enzymes.