The densest k-subgraph problem has been well-studied, and significant work has been put into developing approximation algorithms and
hardness results for it. The problem is of theoretical interest, because it is often used in reductions to other approximation problems, and it
also has practical applications to tasks like community detection in social networks. This research focuses on developing approximation algorithms for the much less studied hypergraph generalization of densest k-subgraph. In this presentation, we will review the state of the art algorithms for two and three uniform hypergraphs, and present new results from our research.