The theory of matroids over hyperfields generalizes both combinatorial ideas such as matroid and oriented matroid theory and finite-dimensional vector spaces. The Grassmannian Gr(r, Fⁿ) over a hyperfield F is interesting from both of these perspectives. I will discuss joint work with Jim Davis on topologically relating various hyperfields—including the real and complex numbers, more combinatorial “shadows” of these, and “tropicalizations” of these—and their associated Grassmannians.