In this thesis we considered problems of Turaan type for hypergraphs. First we showed the classic results of this type for graphs, Turan’s and Erdos-Stone theorem. Afterwards we introduced the basic notions related to hypergraphs. We defined the Turan density of a uniform hypergraph and showed the basic results on Turan density of degenerate hypergraphs, supersaturation and blowing-up. We introduced the concept of iterated blow-ups and demonstrated some constructions giving important lower bounds on Turan density. Next, we demonstrated some of the methods for determining the Turan density of hypergraphs. We introduced links, and used the link method to determine the Turan density of the Fano plane. We also showed that the Turan density of a family of hypergraphs can be less than the Turan density of each member of the family and proved a simple upper bound on the density of the tight cycle of length 5. We briefly presented the proofs of two new results in this area which use the method of coloring the shadow of a hypergraph and the stability method. We then demonstrated the stability method on the example of a cycle and showed some of its applications. In the end, we presented several open problems of Turan type that are connected to the results presented in this thesis.