In this talk we will introduce the decomposition of the Grassmannian G_kn into Schubert cells, indexed by partitions fitting inside a k by (n-k) rectangle. We will also look at the decomposition into matroid strata, also known as Gelfand-Serganova strata, which is a refinement of the Schubert decomposition. If time permits, we will examine the totally nonnengative Grassmannian.