  I present quenched domain wall fermion and 2+1 flavor improved Kogut-Susskind fermion calculations of the hadronic vacuum polarization which are used to calculate the ${\cal O}(\alpha^2)$ hadronic contribution to the anomalous magnetic moment of the muon. Together with previous quenched calcuations, the new results confirm that in the quenched theory the hadronic contribution is signifcantly smaller ($\sim 30%$) than the value obtained from the total cross section of $e^+e^-$ annhilation to hadrons. The 2+1 flavor results show an increasing contribution to $g-2$ as the quark mass is reduced. 
Lattice calculation of the lowest-order hadronic contribution to the   muon anomalous magnetic momen