Failure in adhesive joints is usually the result of the non-uniform distribution of stresses that generally appears along the bond-lines, with peak values near the ends of the overlaps and inner zones where the adhesive essentially does not work. For joints comprised of dissimilar materials, the stress fields are also affected by the absence of symmetry. The present work is focused on "functionally graded adhesive joints" to avoid this phenomenon and to improve the strength of aluminum/composite joints under shear loads. Looking for the most favorable grading of properties, a search/optimization procedure is implemented based on finite element calculations and considering continuous variations of the material responses within the adhesive layer. After this, a comparative analysis of the continuous distributions obtained against discrete/"banded" approximations is performed, as these configurations are more feasible for manufacturing and therefore more suitable for industrialization. In order to avoid singularities appearing in the "banded" solutions simulations, a numerical strategy is proposed to model the transitions between the different adhesive phases.