TITLE: What can we learn from the tropicalization of an algebraic variety?
QUESTION [37 upvotes]: I often hear people speaking of the many connections between algebraic varieties and tropical geometry and how geometric information about a variety can be read off from the associated tropical variety. Although I have seen some concrete examples of this, I am curious about how much we can get out of this correspondence in general. More precisely, my question is the following:

Which information of $X=V(I)$ can be
  read off its tropicalization
  $\mbox{Trop(X)}=\bigcap_{f\in I}\mbox{trop}(f)$?

As a very basic example,  it is known that $\dim(X)=\dim_{\mathbb{R}}\mbox{Trop}(X)$.

REPLY [5 votes]: In arxiv.org/0805.1916 Sam Payne shows that one can reconstruct the analytification of a quasiprojective variety over a nonarchimedean field as the inverse limit of its tropicalisations.