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Score following is the synchronisation of a computer with a performer playing a known musical score. It now has a history of about twenty years as a research and musical topic, and is an ongoing project at Ircam. We present an overview of existing and historical score following systems, followed by fundamental definitions and terminology, and considerations about score formats, evaluation of score followers, and training. The score follower that we developed at Ircam is based on a Hidden Markov Model and on the modeling of the expected signal received from the performer. The model has been implemented in an audio and a Midi version, and is now being used in production. We report here our first experiences and our first steps towards a complete evaluation of system performances. Finally, we indicate directions how score following can go beyond the artistic applications known today.