Voice control in the smart home is commonplace, enabling the convenient control of smart home Internet of Things hubs, gateways and devices, along with information seeking dialogues. Cloud-based voice assistants are used to facilitate the interaction, yet privacy concerns surround the cloud analysis of data. To what extent can voice control be performed using purely local computation, to ensure user data remains private? In this paper we present a taxonomy of the voice control technologies present in commercial smart home systems. We first review literature on the topic, and summarise relevant work categorising IoT devices and voice control in the home. The taxonomic classification of these entities is then presented, and we analyse our findings. Following on, we turn to academic efforts in implementing and evaluating voice-controlled smart home set-ups, and we then discuss open-source libraries and devices that are applicable to the design of a privacy-preserving voice assistant for smart homes and the IoT. Towards the end, we consider additional technologies and methods that could support a cloud-free voice assistant, and conclude the work.