According to AdS/CFT a remarkable correspondence exists between strings in AdS5 x S5 and operators in N=4 SYM. A particularly important case is that of fast-spinning folded closed strings and the so called twist-operators in the gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability properties. In this talk I will show how to match the expression of the anomalous dimension of twist operators as computed from the quantum superstring with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability.