Concatenative sound synthesis is a promising method of musical sound synthesis with a steady stream of work and publications for over five years now. This article offers a comparative survey and taxonomy of the many different approaches to concatenative synthesis throughout the history of electronic music, starting in the 1950s, even if they weren't known as such at their time, up to the recent surge of contemporary methods. Concatenative sound synthesis methods use a large database of source sounds, segmented into units, and a unit selection algorithm that finds the units that match best the sound or musical phrase to be synthesised, called the target. The selection is performed according to the descriptors of the units. These are characteristics extracted from the source sounds, e.g. pitch, or attributed to them, e.g. instrument class. The selected units are then transformed to fully match the target specification, and concatenated. However, if the database is sufficiently large, the probability is high that a matching unit will be found, so the need to apply transformations is reduced. The most urgent and interesting problems for further work on concatenative synthesis are listed concerning segmentation, descriptors, efficiency, legality, data mining, and real time interaction. Finally, the conclusion tries to provide some insight into the current and future state of concatenative synthesis research.