  Using the 2+1 flavor Nambu--Jona-Lasinio (NJL) model with the Polyakov loop,
we determine the structure of the QCD phase diagram in an external magnetic
field. Beyond the usual NJL model with constant couplings, we also consider a
variant with a magnetic field dependent scalar coupling, which reproduces the
Inverse Magnetic Catalysis (IMC) at zero chemical potential. We conclude that
the IMC affects the location of the Critical End Point, and found indications
that, for high enough magnetic fields, the chiral phase transition at zero
chemical potential might change from an analytic to a first-order phase
transition.
