I talk about finite corrections to the large spin asymptotics of N=4 SYM twist operators. These corrections are an all-loop result, not affected by wrapping effects, and agree, after determining the strong coupling expansion, with string theory predictions. The finite order corrections enter the sub-leading poles of the logarithm of multi loop gluon scattering amplitudes and describes the difference between the former and the expectation value of certain Wilson lines. For the complete sub-leading pole structure however a second function is needed. A few comments on the quest for a search of a possible description of the latter in terms of local operators will be given.