The proliferation of internet-connected mobile devices will continue to drive growth in data traffic in an exponential fashion, forcing network operators to dramatically increase the capacity of their networks. To do this cost-effectively, a paradigm shift in cellular network infrastructure deployment is occurring away from traditional (expensive) high-power tower-mounted base stations and towards heterogeneous elements. Examples of heterogeneous elements include microcells, picocells, femtocells, and distributed antenna systems (remote radio heads), which are distinguished by their transmit powers/ coverage areas, physical size, backhaul, and propagation characteristics. This shift presents many opportunities for capacity improvement, and many new challenges to co-existence and network management. This article discusses new theoretical models for understanding the heterogeneous cellular networks of tomorrow, and the practical constraints and challenges that operators must tackle in order for these networks to reach their potential.