The major objective of this article is to present recent advances in the methodology to fine tune the adhesive performance of a PSA. In addition to the so-called Dahlquist criterion requiring a low modulus, we propose two additional rheological predictors of the adhesive properties. The first one is derived from the description of the detachment of a linear elastic layer from a rigid substrate. We made an approximate extension of this analysis to the viscoelastic regime and showed that the transition from interfacial cracks to cavitation and fibrillation can be quantitatively predicted from the easily measurable ratio tan()/G'(). If a fibrillar structure is formed, the nonlinear large strain properties become important. We showed that the ability of the fibrils to be stretched before final debonding can be predicted from the analysis of simple tensile tests. The softening, which occurs at intermediate strains, and, more importantly, the hardening which occurs at large strains, can be used to predict the mode of failure and the energy of adhesion. The use of this methodology to tune the PSA structure for a specific application has been illustrated for the special case of wb-PSA made of core-shell particles, and improved adhesive properties on polyethylene surfaces have been obtained.