Particles or other microdevices are disposed in an array having discreet regions (e.g. magnetic bars), oriented within a magnetic field, and then sorted through application of a removing force under conditions that remove a proper subset of the microdevices from the array as a function of differing orientations of the microdevices. Methods are also contemplated for using magnetic patterns to sort collections of microdevices by magnetic complementarity. Preferred methods use a capture and release process to sort microdevices (microdevices), and unlike conventional sorters, do not require high particle flow rates. Also contemplated are microdevice libraries in which microdevices have mutually distinct magnetic codes, and a region with a mutually distinct polymeric or other chemical moiety.