  After a brief summary of the basic properties of stationary spacetimes
representing rotating, charged black holes in strong axisymmetric magnetic
fields, we concentrate on extremal cases, for which the horizon surface gravity
vanishes. We investigate their properties by constructing simpler spacetimes
that exhibit their geometries near degenerate horizons. Starting from the
symmetry arguments we find that the near-horizon geometries of extremal
magnetised Kerr-Newman black holes can be characterised by just one
dimensionless parameter: "effective Kerr-Newman mixing angle". Employing the
near-horizon geometries we demonstrate the Meissner effect of magnetic field
expulsion from extremal black holes.
