Covering a graph with subgraphs of certain type has a long history and it goes back to Boole, Ore and M. Hall jr. The problem of covering a graph by cliques, bicliques or copies of the same graph has been studied by many researchers including Erdos, Goodman, Posa, Wilson, Chung, Graham, Pollak, Alon etc. Few of the results obtained for graphs extend to hypergraphs. In this talk, I will present some of these known facts and show some new results regarding the covers of an r-uniform hypergraph by k-cuts such that the total size of the cuts (the sum of the number of hyperedges of all cuts) is minimized. This is joint work with André Kündgen (Cal State San Marcos).