Street lighting characterizes many smart city initiatives around the world. In fact, significant savings can be achieved by not only replacing traditional luminaires with low-power LEDs, but also providing streetlights with smart light controllers and network connectivity, allowing the introduction of a sensible light intensity management and reduction of maintenance costs. Moreover, if designed with a far-looking view, smart lighting infrastructure could also support city-wide Internet of Things services, becoming key enablers of the smart city revolution, also in the 5G perspective. In this paper, we provide a thorough discussion on network architectures and communication technologies that could be adopted for smart public lighting applications, showing their benefits and downsides. Starting with significant activity on research, implementation and in-field testing, we also outline the steps required for the deployment of a smart public lighting infrastructure, each discussed in accordance with the network topology considered. Finally, we introduce some additional services that a smart public lighting infrastructure could support and discuss the benefits that would arise from integration with the upcoming 5G cellular network.