In this work, challenges in robust topology optimization of multi-component structures, also called assemblies, are presented, and first solution approaches are discussed. For topology optimization of multi-component structures, the modeling of the connecting joints is crucial. A possibility to treat multi-component optimization is the use of both-sided contact laws for the joints. In contrast, in this talk the framework for unilateral contact-constrained topology optimization is extended to model the connecting joints. In doing so, several components of an assembly are simultaneously optimized, whereby the compliance is minimized. Here, only compressive forces are transmitted at the joints. This allows to remove non-design spaces at the joint, since the material is only distributed along the loading path inside the component. The proposed method is applied to benchmark examples and the impact of different engineering fits at the joints are investigated. It turns out, that the optimized designs are essentially different, depending on the engineering fits. This observation motivates robust topology optimization, since it can reduce the sensitivity of the topology with respect to the geometry of the joint. In this work, a robust topology optimization approach for contact-constrained structures is extended to multi-component optimization. This approach is based on the framework for contact-constrained topology optimization, as well as the first-order second-moment method. However, the non-smooth characteristic of the contact leads to challenges using Taylor series based methods such as the first-order second-moment method. Here, multimodal approaches seem to be promising to increase the accuracy of Taylor series based methods, since a standard Taylor series neglects the non-smooth characteristic of the contact problem. In contrast, the numerical costs increase significantly if sampling based methods are used for robust topology optimization. Both approaches are compared in regard of obtain designs, robustness and computational costs.