This is a talk presenting dome results on geometrical dualities for MV-algebras. The article is dedicated to the memory of Leo Esakia. The talk was delivered at the Studia Logica conference Ordered Groups and Lattices in Algebraic Logic, Tbilisi, Georgia. $22^{d}$ September, 2011.
A very similar talk was selected as featured talk at the XIX Congess of Italian Mathematicians, Bologna 12-17 September 2011.