Performance is a substantial component of the musical work, adding the physical reality to “fictitious” score symbols and the power of sensorial evidence to the interpretative reflection of analysis. We first discuss the theory of musical interpretation and its performance. Performance transformations from symbolic to physical reality are described by performance vector fields, a generalization of tempo curves. Such fields are shaped by specific performance operators the arguments of which are weight functions issued from music analyses. The action of performance fields is stratified according to hierarchies of musical parameters, such as onset, duration, pitch, loudness, or more complex parameters of instrument and gesture. Performance also unfolds according to the genealogical refinement while rehearsing, and is realized in the mathematical stemma model and implemented in the performance software RUBATO ®. We also present inverse performance theory, which deals with the reconstruction of system parameters that lead to a given performance. More generally speaking, performance may be viewed as a transformation of any symbolic data into its sensorial representation in the ordinary human spacetime. We discuss this extension in the case of “multimedia performance of knowledge” as it occurs in the visualization and auralization of musical and other databases, such as scores or libraries. This subject is a central feature in the ongoing implementation of the Distributed RUBATO ® software for music representation, analysis, composition, and performance.