According to the AdS/CFT duality a remarkable correspondence exists between strings in AdS and operators in N=4 SYM. A particularly important case is that of folded strings and the so called twist-operators in gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability. In this talk I will show how to match the expression of the anomalous dimension of twist operators (cusp anomaly) as computed in string theory 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. I will also comment on the computation of finite size corrections to the cusp anomaly.