The basis of renormalon calculus is briefly discussed. The method is applied to study QCD predictions for three sum rules of deep-inelastic scattering, namely for the Gross-Llewellyn Smith, Bjorken polarized and unpolarized sum rules. It is shown that the renormalon structures of theses sum rules are closely related. These properties are giving us the hint that theoretical expressions of these three sum rules are similar both in the and non-perturbative sectors. Some phenomenological consequances of the new relations are discussed.

16 pages, LaTeX, Extanded version of the talk at 19th Rencontre de Physique de la Vallee d" Aosta (27 February-5 March, 2005, La Thuile, Aosta Valley, Italy); Few additional comments added, several references added, accepted for publication in Mod.Phys.Lett.A as a Brief Review with the title "Deep inelastic sum rules at the boundaries between perturbative and non-perturbative QCD"