Industry and academia agree that brake squeal is a nonlinear phenomenon. Consequently, using solely linear finite-element (FE) models and assessing the tendency of a brake system to squeal exclusively on the stability of the trivial solution is not appropriate. However, the latter approach - in the brake community known as complex eigenvalue analysis (CEA) - is extensively used in industry. Until now, nonlinear simulation approaches considering existence and stability of periodic solutions are mostly limited to minimal models. Among the variety of reasons for this the complexity of large-scale nonlinear models as well as the identification of nonlinear material and system parameters are crucial.This contribution discusses the relevance of nonlinearities in friction brake noise, vibration, harshness (NVH) and presents a novel simulation approach for brake squeal. On the basis of experimental results it is pointed out that the consideration of nonlinearities in simulation as well as new methods for numerical studies are necessary to cope with the system-inherent phenomena. After presenting experimental methods to characterize nonlinearities in brake systems, a novel simulation approach for brake squeal is introduced. This approach is based on subspace projection and allows the calculation of limit cycles considering nonlinearities such as joint damping. Studies are conducted for minimal models and a full-scale industrial FE model.