I will review different setups to study representation stability for complex representations of the finite linear group
$GL_n(\mathbb{F}_q): VI-modules, modules over $GL_{\infty}(\mathbb{F}_q)$ and interpolation categories $Rep GL_t(\mathbb{F}_q)$ for a complex number t in the sense of Deligne. Most of my talk will focus on the latter. This is joint work with Inna Entova-Aizenbud.