Selective adhesion between surfaces is a highly desirable property for many practical applications. The ability to control adhesion selectivity by design of near-surface architecture irrespective of surface chemistry is broadly appealing. The first chapter shows that highly selective interfacial properties can be achieved between surfaces patterned with complementary micro-channel structures: strongly enhanced work of adhesion between two matched patterns and highly attenuated adhesion between most others. Relative misalignment is accommodated by screw dislocations that run in a direction orthogonal to the channels. Dislocation energy governs the width of dislocation core; misorientation controls dislocation distribution through the Moire pattern of pillar/channel combinations on the two sides of the interface. This versatile system could be a useful experimental tool in assisting research on geometrycontrolled adhesion, while providing a test-bed for stability theories of interacting dislocations and crack fronts. The second chapter studies the adhesion selectivity by electrostatic complementarity. We consider the interaction between two flat surfaces separated by water in the presence of ions, each with simple striped pattern of alternating positive and negative surface charges, and each with zero net charge. We show that such surfaces have highly selective adhesion depending on the matching between the two charge patterns. Because a number of problems related to micro-structured surfaces require analysis of their contact mechanics and extraction of material properties of indentation ex- periments, the third chapter provides a complete numerical simulation package that allows for general analysis of the contact problems involving complex geometry. To solve the system of a large number of highly nonlinear equations, a virtual state relaxation method has been used by interposing a virtual dash-pot in the mechanical system. This method plots only the stable equilibriums for each displacement, and therefore the load-displacement curves are discontinuous at unstable jumps. It essentially generates the force-displacement curves that can be observed in real-world experiments.