A theory for the growth of columnar microstructures in thin films is presented. The zone-I to zone-II transition temperature is predicted. The surface morphology and the columnar grain structure are obtained both analytically and numerically, and the scaling behavior of the columnar grain size with film thickness is derived. Monte Carlo simulations are used to follow the evolution of the three-dimensional zone-II microsctuctures and to account for the formation of film texture. These results agree with experimental observations.