Matroids are a combinatorial abstraction of the notion of independence in mathematics introduced inde-pendently by Whitney and Nakasawa. Some examples come from the theory of graphs and linear algebra, however mostexamples do not arise in this fashion. There is however one geometric setting in which matroids from any area of mathematics live, and that is in the world of tropical algebraic geometry. This geometry is polyhedral in nature and therefore looks very different from usual algebraic geometry over say the real or complex numbers. I will show how some combinatorial matroid invariants appear as geometric invariants in this setting and how this gives a powerful approach to study them.