It is well known that nanomagnetics could greatly improve data storage. In this work, through theory and experiment, we show that nanomagnetic patterned arrays are equally promising for data processing. Such arrays offer many potential advantages over CMOS circuits of the same scale: power dissipation drops through magnetostatic signal transport replacing resistive and radiative transmission lines; noise resistance is increased by low environmental coupling; interconnection problems are mitigated by signal transfer via "wireless" interactions. Magnetic interaction simulations using typical parameters suggest that room temperature operation is feasible. Experimental evidence and first-principles analysis will be presented to support this finding. We demonstrate specific nanomagnetic arrays which exhibit basic logic functions. We also show that the implementation of these arrays is within the reach of a hybrid strategy of e-beam lithography and a new non-lithographic nanofabrication technique our lab has developed (to be described in a separate report). Modeling collective behavior and designing nanomagnetic array logic represent new challenges which are met by a full-interaction-matrix Monte Carlo technique we developed. This approach enables simulation of nanodisk lattices as well as engineered branched arrays and gates for general logic. Unlike a nearest-neighbor model, our approach includes all interactions; thus, we may predict and compensate for problems arising from long-range interactions which arise in large circuits. In conclusion, magnetic nanostructures and nano-array gates show significant promise for nanoscale, room-temperature information processing.