The behavior of the $\phi$ meson in nuclear matter has attracted renewed interest because of (recent and future) experiments that aim to study the $\phi$ meson properties in nuclei.
Theoretically, many works have however been conducted for the $\phi$ meson at rest with respect to the nuclear medium. In these proceedings, I will review recent theoretical progress related to this topic. Non-zero momentum effects will be especially relevant for future experiments, such as E16 at J-PARC, where the $\phi$ meson will not be measured at rest, but with finite momentum with respect to
the surrounding nucleus.