In this talk we will discuss two invariants of singularities: The complexity and the rank. It was conjectured by Shokurov that the complexity is non-negative, and is zero if and only if the singularity is formally toric. In this talk we will explain a recent proof of this conjecture by Roberto Svaldi and the speaker. Then, we proceed to explain the Jordan property for the fundamental group of klt singularities and how this property allows us to introduce a new invariant called the rank of the singularity.FInally, we sketch how singularities of full rank and large p-torsion can be degenerated in some sort of quotient singularities. In order to prove this later statement, the complexity plays an important role.