Millimeter wave (mmW) frequencies between 30 and 300 GHz are a new frontier for cellular communication that offers the promise of orders of magnitude greater bandwidths combined with further gains via beamforming and spatial multiplexing from high-dimensional multi-element antenna arrays.  This talk surveys measurements and capacity studies in New York City at 28 and 73 GHz demonstrate that mmW systems can offer more than an order of magnitude increase in capacity over current state-of-the-art 4G cellular networks at current cell densities. Cellular systems, however, will need to be significantly redesigned to fully achieve these gains. The talk discusses how various technologies including adaptive beamforming and multihop relaying can be leveraged in the mmW context.