Led by the success of neural style transfer on visual arts, there has been a rising trend very recently in the effort of music style transfer. However, "music style" is not yet a well-defined concept from a scientific point of view. The difficulty lies in the intrinsic multi-level and multi-modal character of music representation (which is very different from image representation). As a result, depending on their interpretation of "music style", current studies under the category of "music style transfer", are actually solving completely different problems that belong to a variety of sub-fields of Computer Music. Also, a vanilla end-to-end approach, which aims at dealing with all levels of music representation at once by directly adopting the method of image style transfer, leads to poor results. Thus, we vitally propose a more scientifically-viable definition of music style transfer by breaking it down into precise concepts of timbre style transfer, performance style transfer and composition style transfer, as well as to connect different aspects of music style transfer with existing well-established sub-fields of computer music studies. In addition, we discuss the current limitations of music style modeling and its future directions by drawing spirit from some deep generative models, especially the ones using unsupervised learning and disentanglement techniques.