Delta-matroids are type B generalizations of matroids in the theory of Coxeter matroids. We generalize many recent developments in the algebraic geometry of matroids to that of delta-matroids. These include the theory of tautological classes of delta-matroids, and formulas for volumes of type B generalized permutohedra. In particular, for a class of delta-matroids that includes all graphical delta-matroids, we show a log-concavity for "Tutte polynomials" of delta-matroids. Time permitting, we'll indicate some future directions in the pursuit of a "Hodge theory" for Coxeter matroids.