Microalgae have traditionally been used in many biotechnological applications, where each new application required a different species or strain expressing the required properties; the challenge therefore is to isolate or develop, characterize and optimize species or strains that can express more than one specific property. In agriculture, breeding of natural variants has been successfully used for centuries to improve production traits in many existing plant and animal species. With the discovery of the concepts of classical genetics, these new ideas have been extensively used in selective breeding. However, many biotechnologically relevant algae do not possess the sexual characteristics required for traditional breeding/crossing, although they can be modified by chemical and physical mutagens. The resulting mutants are not considered as genetically modified organisms (GMOs) and their cultivation is therefore not limited by legislation. On the other hand, mutants prepared by random or specific insertion of foreign DNA are considered to be GMOs. This review will compare the effects of two genetic approaches on model algal species and will summarize their advantages in basic research. Furthermore, we will discuss the potential of mutagenesis to improve microalgae as a biotechnological resource, to accelerate the process from specific strain isolation to growth optimization, and discuss the production of new products. Finally, we will explore the potential of algae in synthetic biology.