  This paper provides an overview of recent progress on the interplay between
tropical geometry and non-archimedean analytic geometry in the sense of
Berkovich. After briefly discussing results by Baker, Payne and Rabinoff in the
case of curves, we explain a result by Cueto, H\"abich and the author comparing
the tropical Grassmannian of planes to the analytic Grassmannian. We also give
an overview of the general higher-dimensional theory developed by Gubler,
Rabinoff and the author. In particular, we explain the construction of
generalized skeleta in which are polyhedral substructures of Berkovich spaces
lending themselves to comparison with tropicalizations. We discuss the slope
formula for the valuation of rational functions and explain two results on the
comparison between polyhedral substructures of Berkovich spaces and
tropicalizations.
