Conformal antennas are defined as antennas that conform to the structure for other reason than electromagnetic. This reason can be aerodynamic, hydrodynamic, aesthetic, coverage reason or to obtain improved radiation properties. Because of these potential advantages over planar antennas conformal microstrip patch antennas have been proposed for a wide range of applications, eg. for smart base station, airborne radars, rockets, satellite tracking system, etc. The conformal arrays can scan the beam without drop of the gain, and the size of the conformal antenna needed for obtaining the same gain as its planar counterpart is approximately the same. Spherical arrays have possibility of directing single or multiple beams through complete hemisphere and, therefore, spherical arrays are an attractive solution for satellite tracking, telemetry, etc. On other hand, microstrip antennas have lot of good properties like possibility to conform to the structure, thin profile, light weight, low cost and simple manufacturing. Therefore, one possible and simple realization of a spherical array is to use patch elements on a spherical supporting structure. In the thesis we have studied the spherical arrays of rectangular and circular microstrip antennas embedded in or placed on a general multilayer spherical structure. The analysis approach is based on solving the integral equation for electric field by using the moment method. The solution procedure takes advantage of spectral-domain approach where the three-dimension problems is transformed into spectral of much simpler one-dimension problems. In the solution procedure the spherical multilayer structure is rigorously taken into account by calculating appropriate spectral-domain Green’s functions. The main disadvantage of spectral-domain method is numerical unstability appearing in the analysis of spherical structure with large radius. In order to avoid numerical problems a modified vector-Legendre transformation and normalized Legendre polynomials are defined and applied to the solution procedure. Furthermore, an approximate method is developed to calculate mutual coupling between arrays element with intention to decrease the needed computer calculation time. Moreover, the comparison of spherical and cylindrical patch antennas is given in order to show the importance of rigorous analysis of patch antennas on curved structures where both principal curvatures are different from zero. The influence of structure radius on input impedance, mutual coupling and radiation pattern was also investigated. We have made the program for calculating input impedance, mutual coupling and radiation pattern of spherical patch arrays based on developed spectral-domain approach. Furthermore, a laboratory model is built to test properties of different patch configurations and to validate accuracy of developed program. The calculated and measured values are in good agreement in all considered cases.