The paper is concerned with the modelling as well as the optimization of adhesively bonded joints. Engineering structures consist of many different elements that need to be jointed together in order to form a load transfer path. Although there are many joint methods, bonding using adhesive layers offers several advantages, including the capacity to join different materials and enable the assembly to enhance its mechanical properties, improving those of the individual constituent materials, and meeting specific requirements for strength and comfort. Consequently, adhesive bonding technology has found extensive application in lightweight aerospace or automotive structures. The joint is constituted by two elastic materials separated by a thin adhesive layer. After defining a small parameter tending to zero associated with the thickness and the constitutive coefficients of the intermediate layer, the variational limit model governing the deformation of the materials subject to shear and tensile loads is formulated. The structural optimization problem for this state problem is formulated. This problem consists in finding the design domain occupied by the adherents or the distribution of the material density function within the design domain occupied by adherents to minimize the elastic energy of the bonded bodies and to redistribute the stress peaks, occurring at the ends of adhesive layer overlap, in favor to the load capacity. The necessary optimality condition is formulated. The level set approach is proposed to track the evolution of the design domain and to find the optimal topology minimizing the peel as well as the shear stresses. Details of the numerical implementation are reported. Numerical results are reported and discussed.