Furstenberg's theorem for random matrix products has been a key tool in many contexts, including mathematical physics. Of particular interest is the 1-dimensional Anderson model of electron diffusion in random media. In this talk, we will discuss how to apply a version of Furstenberg's theorem where matrices are independent but not necessarily identically distributed (non-stationary). In particular, we will discuss how to prove spectral and dynamical localization in the non-stationary Anderson model with unbounded potentials using this version of Furstenberg's theorem.