Estimating the position of mobile devices with high accuracy in indoor environments is of interest across a wide range of applications. Many methods and technologies have been proposed to solve the problem but, to date, there is no "silver bullet". This paper surveys research conducted on indoor positioning using time-based approaches in conjunction with the IEEE 802.11 Wireless Local Area Network standard (WiFi). Location solutions using this approach are particularly attractive due to the wide deployment of WiFi and because prior mapping is not needed. This paper provides an overview of the IEEE 802.11 standards and summarizes the key research challenges in 802.11 time-based positioning. The paper categorizes and describes the many proposals published to date, evaluating their implementation complexity and positioning accuracy. Finally, the paper summarizes the state-of-the-art and makes suggestions for future research directions.