Concatenative synthesis is a promising method of musical sound synthesis with a steady stream of work and publications in recent years. Concatenative sound synthesis methods use a large database of source sounds, segmented into heterogeneous 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. We explain its principle and components and its main applications, and compare existing concatenative synthesis approaches. We then list the most urgent problems for further work on concatenative synthesis.