  Mustafin varieties are flat degenerations of projective spaces, induced by a
choice of an $n-$tuple of lattices in a vector space over a non-archimedean
field. They were introduced by Mustafin in the 70s in order to generalise
Mumford's groundbreaking work on the unformisation of curves to higher
dimension. These varieties have a rich combinatorial structure as can be seen
in pioneering work of Cartwright, H\"abich, Sturmfels and Werner. In this
paper, we introduce a new approach to Mustafin varieties in terms of images of
rational maps, which were studied by Li. Applying tropical intersection theory
and tropical convex hull computations, we use this method to give a new
combinatorial description of the irreducible components of the special fibers
of Mustafin varieties. This enables connections to various topics. In
particular, we see that any multiview variety appears as an irreducible
component of the special fiber of some Mustafin variety. Furthermore, we use an
interpretation of Mustafin varieties as a moduli functor introduced by Faltings
to relate them to certain moduli functors, called linked Grassmannians. These
objects are featured in limit linear series theory. The focal point of study
regarding linked Grassmannians are so-called \textit{simple points}. As a
direct consequence of the new combinatorial description of Mustafin varieties,
we prove that the simple points of linked Grassmannians are dense in every
fiber. Finally, we use the connection to linked Grassmannians, to relate the
special fibers of Mustafin varieties to certain local models of unitary Shimura
varieties.
