Coxeter groups form an abstraction of groups generated by reflections in a real vector space. To every Coxeter group corresponds a root system enclosing it geometric and algebraic structure. A root system is a set of vectors of the vector space which is stable under the action of the reflection group. When the group is infinite, so is the root system; giving rise to accumulation points in the projective space. These points are the limit roots of the Coxeter group. Limit roots give a lot of information and intuition on the structure of the group. Curiously, they often form fractals with certain unexplained properties. In this talk, we will present limit roots and related problems of this growing theory.