Since the new generation of radio synthesis arrays are producing a large amount of data with high sensitivity, it is of great interest to devise new calibration techniques to keep up with the quality of the data. I have developed novel statistical calibration algorithms and investigated their properties in order to obtain optimal solutions with the highest possible speed of convergence. The result is calibration that is faster by orders of magnitude than before. In my thesis, these calibration algorithms are presented and the improvement that they achieve is illustrated with both simulated data as well as real data.