Traditionally, the study of the homotopy type of Berkovich  spaces was based upon deep and difficult theorems in  arithmetic geometry. In this talk, we will present a completely  different approach, which is due to Hrushovski and Loeser.  It makes an intensive use of the model theory of valued fields,  and it has (among other things) yielded the following result:  if $X$ is a quasi-projective algebraic variety over a  non-Archimedean, complete field $k$, every semi-algebraic  subset of the Berkovich space associated to $X$ is locally  contractible, and has the homotopy type of a compact  polyhedron.