I will start with a general introduction to the theory of matroids. I will then focus on the class of regular matroids, and discuss how some ideas from chip-firing games extend from graphs to these matroids. For example, for such matroids one can define Jacobian groups whose cardinality/volume is related to the "complexity" of the matroid. I will end by introducing a very general class of bijections between Jacobian elements and bases elements. Although these bijections are described purely combinatorially, it turns out that there is a very beautiful geometry behind the scenes.