The CLR inequality provides an upper-bound on the number of negative eigenvalues of a Schrödinger operator, $-\Delta-V$ in $L^2(\mathbb{R}^d)$, for dimension $d\geq 3$ in terms of the $L^{d/2}(\mathbb{R}^d)$-norm of its potential. In dimensions one and two there is an absence of such bounds since any non-trivial potential $V$ always produces at least one negative eigenvalue. In this talk I will consider the case of the two dimensional Schrödinger operator with an Aharonov-Bohm magnetic field. We will see that the addition of this magnetic field lifts the energy enough for us to find CLR type bounds. The results discussed are from joint works with Rupert L. Frank, Ari Laptev and Lukas Schimmer.