  In the literatur there exist approximation methods for McKean-Vlasov
stochastic differential equations which have a computational effort of order
$3$. In this article we introduce full-history recursive multilevel Picard
(MLP) approximations for McKean-Vlasov stochastic differential equations. We
prove that these MLP approximations have computational effort of order $2+$
which is essentially optimal in high dimensions.
