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We give a detailed microscopic derivation of gauge and stringy instantongenerated superpotentials for gauge theories living on D3-branes atZ_3-orientifold singularities. Gauge instantons are generated by D(-1)-branesand lead to Affleck, Dine and Seiberg (ADS) like superpotentials in theeffective N=1 gauge theories with three generations of bifundamental andanti/symmetric matter. Stringy instanton effects are generated by EuclideanED3-branes wrapping four-cycles on T^6/\Z_3. They give rise to Majorana massesin one case and non-renormalizable superpotentials for the other cases. Finallywe determine the conditions under which ADS like superpotentials are generatedin N=1 gauge theories with adjoints, fundamentals, symmetric and antisymmetricchiral matter.

D-brane Instantons on the T^6/Z_3 orientifold