  In this article, we construct SL$_k$-friezes using Pl\"ucker coordinates,
making use of the cluster structure on the homogeneous coordinate ring of the
Grassmannian of $k$-spaces in $n$-space via the Pl\"ucker embedding. When this
cluster algebra is of finite type, the SL$_k$-friezes are in bijection with the
so-called mesh friezes of the corresponding Grassmannian cluster category.
These are collections of positive integers on the AR-quiver of the category
with relations inherited from the mesh relations on the category. In these
finite type cases, many of the SL$_k$-friezes arise from specialising a cluster
to 1. These are called unitary. We use Iyama-Yoshino reduction to analyse the
non-unitary friezes. With this, we provide an explanation for all known friezes
of this kind. An appendix by Cuntz and Plamondon proves that there are 868
friezes of type $E_6$.
