Simplest models of the Universe predict global (statistical) isotropy on large scales in the observable Universe. However there are a number of interesting models that predict existence of preferred directions. In this talk I will present results of using CMB anisotropy maps to test the global isotropy of the Universe on its largest scales, and will show how that can help us constrain interesting models such as topology of the Universe and anisotropic cosmological models (e.g. Bianchi models). I will also discuss the intriguing lack of power on large angular scales in the observed CMB maps and implications that it may have for cosmology.