Adhesion between a flat solid and a rubber is considerably increased by grafting chains (chemically identical to the rubber) on the solid surface. Similarly, a population of mobile chains dissolved into rubber can increase the strength of a rubber/rubber contact. A third (more recent) type of promoter is a "Guiselin brush", obtained by incubating certain polymer melts against a suitable solid. A major practical problem is to understand how the adhesive energy varies with the surface concentration sigma of "connector molecules" : very often, at high connector density, the strength goes down. We set up a theoretical picture of polymer interdigitation, covering most of the cases listed above. We also describe peeling measurements of the adhesion energy G(sigma) for Guiselin brushes (silica/PDMS/PDMS network). For the Guiselin brush, the statistical problem is much more complex. The main experimental result is the presence of a clear maximum in the plot of G(sigma).