Research toward powerful information processing systems that circumvent the interconnect bottleneck by exploiting the nonlinear evolution of multiple phase dynamics in locally connected arrays is discussed. We focus on a scheme in which logic states are defined by the electrical phase of a dynamic process and information processing is realized through interactions between the elements in the array. Simulation results are given for networks comprised of neuron-like integrate-and-fire elements, which could potentially be implemented by ultra-small tunnel junctions, molecules and other types of nanoscale elements. This approach could lead to powerful information processing systems due to massive parallelism in simple, highly scalable nano-architectures. The rational for this approach, its advantages, simulation results, critical issues, and future research directions are discussed.