Phase transitions are among the most striking phenomena of nature. While continuously changing a parameter, like the temperature, the system shows singular behavior at the transition point while a substantial change in the physical properties of the system is found. At a continuous phase transition the degrees of freedom become macroscopically correlated at the critical point, thus the emerging critical singularities are powerful manifestations of collective phenomena. The most impressive property of continuous phase transitions is their universality: the critical behavior is often insensitive to microscopic details, depending only on global characteristics, such as the number of spatial dimensions, the range of interactions and the symmetries of the system. Consequently, it is often sufficient to study a simplified model instead of a realistic system in order to obtain its critical properties. Spatial inhomogeneities, such as dislocations or impurities are inevitable features of realistic systems. Do we have to incorporate also disorder in the models to describe critical phenomena at large scales then, or is it just one of the many unimportant microscopic details? In our research we show that disorder may dramatically change the critical behavior known in the clean, disorder-free system, leading to exotic phenomena.