I will review results regarding the QCD Phase Diagram in the presence of a magnetic background field, based on lattice QCD simulations. In particular, I will discuss recent numerical evidence that the thermal QCD crossover turns into a first order transition for large enough magnetic fields. The critical endpoint is found to be located between eB = 4 GeV^2 and 9 GeV^2, with the corresponding critical temperature ranging between 100 and 60 MeV.