The Feynman-Kac formula represents solutions of linear partial differential equations (PDEs) as expectations and these are approximated by the central limit theorem for iid random variables. The resulting method is called Monte Carlo method and overcomes the so-called curse of dimensionality (the effort does not grow exponentially in the dimension). It was a long-standing problem to find a method which also overcomes the curse of dimensionality for nonlinear PDEs. In this talk we introduce multilevel Picard approximations and explain their success in the approximation of high-dimensional semilinear PDEs.