Motivated by extreme value theory, max-linear graphical models have been recently introduced and studied as an alternative to the classical Gaussian or discrete distributions used in graphical modeling. We present max-linear models naturally in the framework of tropical geometry. This perspective allows us to shed light on some known results and to prove others with algebraic techniques. In particular, we rephrase parameter estimation for max-linear models in terms of cones in the tropical eigenspace fan. This is joint work with Claudia Klüppelberg, Steffen Lauritzen and Ngoc Tran.