Adler Function, DIS sum rules and Crewther Relations

The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(αs4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(αs4) contribution to the singlet part of the Adler function.