In this study, we propose a theory of rough adhesive contact of viscoelastic materials in steady-state sliding. By exploiting a boundary formulation based on Green function approach, the unknown contact domain is calculated by enforcing the local energy balance at the contact edge, thus considering also the non-conservative work of internal stresses which is directly related to the odd part of the Green function. Theoretical predictions indicate that viscoelasticity may enhance the adhesive performance depending on the sliding velocity, thus leading to larger contact area and pull-off force compared to the equivalent adhesive elastic case The interplay between viscoelasticity and adhesion also affects the overall friction. Indeed, at low velocity, friction is strongly enhanced compared to the adhesiveless viscoelastic case, mainly due to the small-scale viscoelastic hysteresis induced by the adhesive neck close to the contact edge At higher velocity, the effect of viscoelastic hysteresis occurring at larger scales (bulk material) leads to even higher friction. Under these conditions, in the presence of adhesion, the small-scale and large-scale viscoelastic contributions to friction cannot be separated. Finally, in contrast with usual predictions for crack propagation/healing in infinite systems, we found a non-monotonic trend of the energy release rates at the trailing and leading contact edges, which is consistent with the finiteness of the contact length. All the presented results are strongly supported by existing experimental evidences.