Abstract: In this paper we summarize our modelling efforts for cosmic rays near the heliopause, and discuss whether galactic cosmic ray modulation beyond the heliopause is possible and present an explanation for the anisotropic nature of the observed cosmic ray intensities in the very local interstellar medium. We show that (i) modulation beyond the heliopause is possible, but highly dependent on the assumed parameters (most notable, the perpendicular diffusion coefficient). Treating the heliopause as a tangential discontinuity, significantly damps this modulation effect and leads to modelled results that are similar to Voyager 1 observations. (ii) By choosing an appropriate functional form of the perpendicular diffusion coefficient on the pitch-angle level, we are able to account for the anisotropic behaviour observed for both galactic and anomalous cosmic rays in the local interstellar medium.