Systems and methods for assembling a structure onto a substrate include an array of programmable magnets disposed beneath a substrate, wherein a magnetic field is applied to the structure to levitate the structure above the substrate while the structure is moved relative to the substrate to align the structure with a corresponding recess formed in the substrate. A magnetic field may be applied to translate and rotate the structure relative to the substrate. Differences between or among the programmable magnets regarding magnetic polarity, energized versus de-energized status, and magnetic field strength may be used to move the structure relative to the substrate in conjunction with a closed-loop control system. A bonded substrate assembly and a method of bonding a first wafer to a second wafer include wherein the first wafer includes a projection and the second wafer includes a matching depression. The first and second wafers are bonded together at least in part via magnetic attraction between respective magnetic layers in the projection and the depression.