Matroids are combinatorial objects, whose axioms attempt to capture possible independence relations among a finite set of vectors. It turns out that this is impossible to do. In fact, as the size of the base set grows larger, the probability that a matroid cannot be realized by a set of vectors approaches 1. We will review the definition of a matroid and talk about tropical Grassmannians and Dressians, and their positive parts. We will conclude with the result that all positively oriented matroids are realizable (Ardila-Rincon-Williams, 2017).