This talk will focus on the circuit axioms of matroid theory. I will start with a short introduction to matroids. I will then present a new strengthening of the circuit axioms that requires the elimination property only among modular pairs of circuits, and show how it can be cryptomorphically phrased in terms of Crapo's axioms for flats. This new point of view leads to a corresponding strengthening of the signed circuit axioms for oriented matroids.