  This paper is a collection of thoughts and observations, being partly a
review and partly a report of current research, on recent work in various
aspects of Gr\"unbaum colorings, their existence and usage. In particular, one
of the most striking significances of Gr\"unbaum's Conjecture in the
2-dimensional case is its equivalence to the 4-Color Theorem. The notion of
Gr\"unbaum coloring is extended from the 2-dimensional case to the case of
arbitrary finite hyper-dimensions.
