Mitra and Epureanu have written a very good and complete overview on nonlinear vibrations of turbine blades. Nonlinearities due to friction and contact mechanics are the main focus. Questions related to modeling and model reduction are particularly addressed. This paper begins with an investigation of the vibration behavior of cyclic linear structures, in which a variety of considerations about the occurrence of standing and propagating waves play an important role. Subsequently, several methods of model-order reduction are presented, where cyclic sectors of tuned bladed disks are assumed. The classification of the linear vibration modes according to their nodal diameters (NDs) is explained in detail. Large models with a high number of degrees-of-freedom (DOF) occurring in the field of turbomachinery dynamics lead to very high computational cost. In this context, the authors consider model-order reduction with projection-based methods to be of particular interest. They give an overview of modern projection-based methods and compare them with regard to their respective advantages and disadvantages in the context of bladed disks with nonlinear friction and intermittent contact.