Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the success of these architectures to inductive link prediction with relational hypergraphs, where the task is over k-ary relations, substantially harder than link prediction on knowledge graphs with binary relations only. In this paper, we propose a framework for link prediction with relational hypergraphs, empowering applications of graph neural networks on fully relational structures. Theoretically, we conduct a thorough analysis of the expressive power of the resulting model architectures via corresponding relational Weisfeiler-Leman algorithms and logical expressiveness. Empirically, we validate the power of the proposed architectures on various relational hypergraph benchmarks. The resulting model architectures substantially outperform every baseline for inductive link prediction and also lead to competitive results for transductive link prediction.