This chapter focuses on systems with contact nonlinearities. Dry friction and unilateral contact are ubiquitous in science and technology. Their effect cannot be properly described in a linearized way. Dry friction is commonly the main cause for dissipation in structural dynamics. Impulsive unilateral interactions (impacts) are an important cause for cross-scale energy transfer. Contact is easy to practically realize, but the dynamics of mechanical systems undergoing contact interactions is challenging to accurately predict. Some attractive tools of dynamical systems theory, including the parametrization method for invariant manifolds, are designed for analytic vector fields. Theoretically, they can be applied to regularized contact models. But this might not be a good idea, as shown in this chapter. A two-step procedure will be pursued: First, the initial finite element model will be reduced via component mode synthesis, if needed in combination with a sub-structuring approach. Then a secondary reduction to the invariant manifold associated with a particular nonlinear mode is done. To define a nonlinear mode, the Extended Periodic Motion Concept will be used, as it is applicable to systems featuring bounded differentiability and dissipation. Besides reduction methods, numerical tools for the given problem class are presented, including alternating frequency-time Harmonic Balance, predictor-corrector continuation, and a dedicated time step integration scheme. Applications include friction-damped structures, thin-walled (geometrically-nonlinear) jointed structures, and vibro-impact systems.