A musical performance renders an acoustic realization of a musical score or other representation of a composition. Different performances of the same composition may vary in terms of performance parameters such as timing or dynamics, and these variations may have a major impact on how a listener perceives the music. The analysis of music performance has traditionally been a peripheral topic for the MIR research community, where often a single audio recording is used as representative of a musical work. This paper surveys the field of Music Performance Analysis (MPA) from several perspectives including the measurement of performance parameters, the relation of those parameters to the actions and intentions of a performer or perceptual effects on a listener, and finally the assessment of musical performance. This paper also discusses MPA as it relates to MIR, pointing out opportunities for collaboration and future research in both areas.