Vehicles equipped with GPS localizers are an important sensory device for examining people's movements and activities. Taxis equipped with GPS localizers serve the transportation needs of a large number of people driven by diverse needs; their traces can tell us where passengers were picked up and dropped off, which route was taken, and what steps the driver took to find a new passenger. In this paper we provide an exhaustive survey of the work on mining these traces. We first provide a formalization of the data sets, along with an overview of different mechanisms for pre-processing the data. We then classify the existing work into three main categories: Social dynamics, Traffic dynamics and Operational dynamics. Social dynamics refers to the study of the collective behaviour of a city's population, based on their observed movements; Traffic dynamics studies the resulting flow of the movement through the road network; Operational dynamics refers to the study and analysis of taxi driver's modus operandi. We discuss the different problems currently being researched, the various approaches proposed, and suggest new avenues of research. Finally, we present a historical overview of the research work in this field and discuss which areas hold most promise for future research