We review the theoretical research on the influence of disorder on structure and phase behavior of condensed matter system exhibiting continuous symmetry breaking focusing on liquid crystal phase transitions. We discuss the main properties of liquid crystals as adequate systems in which several open questions with respect to the impact of disorder on universal phase and structural behavior could be explored. Main advantages of liquid crystalline materials and different experimental realizations of random field-type disorder imposed on liquid crystal phases are described.
Keywords: disorder; liquid crystals; nematic-impurities mixture; phase transitions; random field.