The optical properties of anisotropic quantum dots with ellipsoidal shape are investigated and discussed as a function of the dot aspect ratio. The energy spectrum ~ground and many excited states! is calculated and analyzed in comparison with the spherical quantum dot. The optical matrix elements in the dipole approximation and the oscillator strengths for the infrared transitions are shown. The main result is that optical processes significantly depend on the radiation polarization in contrast to nonpolarized processes observed for spherical quantum dots. The dot anisotropy is shown to play a fundamental role in determining the dot properties.