The field of knowledge representation is moving towards more complex and nuanced models, incorporating n-ary relations and hypergraphs to better capture real-world knowledge. This shift is driven by the need to preserve higher-order relational details and entity roles in structured representations. Researchers are exploring various methodologies, including translation-based models, tensor factorisation-based models, and deep neural network-based models, to develop more effective and efficient solutions. The awareness of entity roles and positions in n-ary relations is also becoming a key focus area, with approaches ranging from aware-less to role-aware models. Furthermore, link prediction in N-ary Knowledge Graphs is gaining significant attention, with applications in completing knowledge graphs and improving downstream performance. Noteworthy papers in this area include: ELRUHNA, which proposes an elimination rule-based framework for unsupervised hypergraph alignment, demonstrating higher alignment accuracy and scalability. The paper on inferring adjective hypernyms with language models, which presents a new resource and fine-tunes large language models to predict adjective hypernymy, increasing the connectivity of Open English Wordnet.