In music, the role of the interpreter is to play her/his part manipulating the performance parameters in order to offer a sonic rendition of the piece capable of conveying specific expressive intentions. Since the 1980s there has been a growing interest in computational expressive music performance (EMP). This research field has two fundamental objectives: the understanding of the phenomenon of human musical interpretation and the automatic generation of expressive performances. Rule based, statistical, machine and deep learning approaches have been proposed, most of them devoted to the classical repertoire, in particular to piano pieces. On the contrary, we present an introduction to the role of expressive performance within popular music and to the contemporary ecology of pop music production, based on the use of Digital Audio Workstations (DAWs) and virtual instruments. After an analysis of the tools related to expressiveness commonly available to modern producers we propose a detailed survey of research into the computational EMP field, highlighting the potential and limits of what is present in literature with respect to the context of popular music, which by its nature cannot be completely superimposed on the classical one. In the concluding discussion we suggest possible lines of future research in the field of computational expressiveness applied to pop music.