Tropicalizing vs Compactifying the Torelli map

We will explain the relationship between the compactified Torelli map (as defined by V. Alexeev) and the tropical Torelli map (as defined by the author in a joint work with S. Brannetti and M. Melo, and furthered studied by M. Chan).
This comparison will shed some light on the analogy between the descriptions of the fibers of the two maps, obtained by the author in joint works with L. Caporaso.