The Kronecker coefficients are some natural numbers that naturally arise from the decomposition of the tensor product of two irreducible representations of the symmetric group. Even though they are fundamental in algebra, representation theory and somehow quantum information theory, there are many open problems surrounding the theory of Kronecker coefficients. One such problem is the existence of a combinatorial description of these numbers. In this talk we will briefly describe what Kronecker coefficients are and then we will discuss the complexity of their computation.