Matroids are a structure that abstracts and generalizes linear and algebraic dependency. They can be defined equivalently from various points of view, however the equivalence is not straightforward. The study on the geometry of matroids has been shown to be fruitful. A celebrated geometric object associated to a matroid is the matroid basis polytope. It is the convex hull of indicator vectors of bases. In the realizable case, it is the image of the closure of a torus orbit in the Grassmannian under the moment map. Another remarkable object is the Bergman fan of a matroid, in the realizable case, it is a simplicial fan structure on the tropicalization of the corresponding hyperplane arrangement complement. The long-standing conjecture about log-concavity of characteristic polynomials of matroids was proven by a Hodge theory of it. We aim to investigate matroids and related dependency structures (e.g. gaussoids for gaussian conditional dependency) from geometric points of view and to discover new properties of these structures.