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In the present talk, the strategies to apply the sensitivity analysis method to aerodynamic shape optimization problems of complex geometries are intensively discussed. To resolve the design of complicated aircraft geometries such as high-lift devices, wing/body configurations, overset mesh techniques are adopted. In addition, a noticeable sensitivity analysis method, adjoint approach, which shows very good efficiency and accuracy for aerodynamic design problems, is also introduced. For the incorporation of the adjoint method into the overset mesh system, adjoint formulations are derived for the overset boundary conditions based on linear interpolation. The feasibility of non-conservative adjoint overset boundary conditions for external flow applications is carefully investigated by comparison with a single block design result for the same geometry. Through the several design application problems for realistic aircraft geometries, the present design framework demonstrates its capability and applicability for aerodynamic design of complex geometries