  This is an expository article on the adic tropicalization of algebraic
varieties. We outline joint work with Sam Payne in which we put a topology and
structure sheaf of local topological rings on the exploded tropicalization. The
resulting object, which blends polyhedral data of the tropicalization with
algebraic data of the associated initial degenerations, is called the adic
tropicalization. It satisfies a theorem of the form "Huber analytification is
the limit of all adic tropicalizations." We explain this limit theorem in the
present article, and illustrate connections between adic tropicalization and
the curve complexes of O. Amini and M. Baker.
