Abstract: The Stern–Brocot sequence, known from number-theory, can be studied within the framework of dynamical systems. To do so, the sequence is constructed from a continuous transformation, the Farey mapping. We construct new generalized Stern–Brocot sequences through a generalization of the Farey mapping by means of Hecke triangle groups. In this talk, we introduce these sequences and discuss our recent contributions to the study of their properties, which involves methods from infinite ergodic theory. In particular, we reproduce a distribution result of Keßeböhmer and Stratmann for the classical Stern–Brocot sequence and extend it to our generalized sequences. This is joint work with Marc Keßeböhmer and Anke Pohl.