While the phi meson vacuum properties, such as mass and width, are well known, it is not clear how these properties will change once it is put in a dense environment such as nuclear matter. To study how the phi meson behaves at finite density has been the goal of several past and near future experiments at KEK, COSY-ANKE and J-PARC. Recently, ALICE has also obtained novel experimental data constraining the phi-N interaction. In this talk, I will focus on the in-medium properties of the longitudinal and transverse polarization modes of the phi meson, which due to the breaking of Lorentz symmetry in nuclear matter, can be modified differently. I will review theoretical predictions for these modifications and discuss how the different modes could be measured at the future J-PARC E16 and E88 experiments.