Nested Sequents or Tree-Hypersequents—A Survey

This paper presents an overview of the methods of nested sequents or tree-hypersequents that were originally introduced to provide a comprehensive proof theory for modal logic. The paper retraces the history of how these methods have developed. Its aim is also to present, in an unified and harmonious way, the most recent results that have been obtained in this framework. These results encompass several technical achievements, such as the interpolation theorem and the construction of countermodels. Special emphasis is also given to the application to logics other than the standard modal ones as well as to relations to other proof theoretic formalisms.