The nearest neighbour problem is of practical significance in a number of fields. Often we are interested in finding an object near to a given query object. The problem is old, and a large number of solutions have been proposed for it in the literature. However, it remains the case that even the most popular of the techniques proposed for its solution have not been compared against each other. Also, many techniques, including the old and popular ones, can be implemented in a number of ways, and often the different implementations of a technique have not been thoroughly compared either. This research presents a detailed investigation of different implementations of two popular nearest neighbour search data structures, KDTrees and Metric Trees, and compares the different implementations of each of the two structures against each other. The best implementations of these structures are then compared against each other and against two other techniques, Annulus Method and Cover Trees. Annulus Method is an old technique that was rediscovered during the research for this thesis. Cover Trees are one of the most novel and promising data structures for nearest neighbour search that have been proposed in the literature.