Nowadays smart antennas gain ground and become widely used in applications, where systems need to adapt to the current environment. The phased arrays are applied both in military and civil applications because of their robust features. Using these arrays we have a unique way to form the beams completely electronically, so they have the shape that is best for the current conditions. The thesis presents an overview of antenna systems which operate on the principle similar to this. The first section provides the reader with necessary background on operation of antenna arrays in the desired way, thorugh theoretical derivations over and above the design considerations. Then it gives an overview for the main principle of the phased array systems inlcuding the different beamforming methods and direction of arrival algorithms. In the final section of the thesis, I am going to introduce some measurements which were taken with a system which is also implemented for the demonstartation of previously presented theoretical formulas.