In this talk we consider the coverage of d-dimensional unit hypersphere by the spherical caps. Two main problems are discussed.

In the first problem, one has a given set of caps and needs to check whether the complete hypersphere is covered or not. It is proven that such problem is NP-hard and the recursive algorithm is presented.

The other problem is the construction of the covering set consisting of N identical caps with the minimal angle. This problem have direct applications in covering the globe by N different transmitters and/or satellites. Different construction methods are introduced and the results are discussed.