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Triple Graph Grammars (TGGs) are a technique for defining the correspondence between two different types of models in a declarative way. The power of TGGs comes from the fact that the relation between the two models cannot only be defined, but the definition can be made operational so that one model can be transformed into the other in either direction; even more, TGGs can be used to synchronize and to maintain the correspondence of the two models, even if both of them are changed independently of each other; ie, TGGs work incrementally.

TGGs have been introduced more than 10 years ago by Andy Schürr. Since that time, there have been many different applications of TGGs for transforming models and for maintaining the correspondence between these models. To date, there have been several modifications, generalizations, extensions, and variations. Moreover, there are different approaches for implementing the actual transformations and synchronizations of models. In this paper, we present the essential concepts of TGGs, their spirit, their purpose, and their fields of application. We also discuss some of the extensions along with some of the inherent design decisions, as well as their benefits and caveats. All these are based on several year’s of experience of using TGGs in different projects in different application areas.