Corpus-based concatenative methods for musical sound synthesis have attracted much attention recently. They make use of a variety of sound snippets in a database to assemble a desired sound or phrase according to a target specification given in sound descriptors or by an example sound. With ever-larger sound databases easily available, together with a pertinent description of their contents, they are increasingly used for composition, high-level instrument synthesis, interactive exploration of a sound corpus, and others. This paper gives an overview of the components needed for corpus-based concatenative synthesis, and details of some realisations. Signal processing methods are crucial for all parts of analysis, (segmentation and descriptor analysis), for synthesis, and can intervene in the selection part e.g. for spectral matching.