  We use the AdS/CFT correspondence to argue that large dyonic black holes in
anti-de Sitter spacetime are dual to stationary solutions of the equations of
relativistic magnetohydrodynamics on the conformal boundary of AdS. The dyonic
Kerr-Newman-AdS_4 solution corresponds to a charged diamagnetic fluid not
subject to any net Lorentz force, due to orthogonal magnetic and electric
fields compensating each other. The conserved charges, stress tensor and
R-current of the fluid are shown to be in exact agreement with the
corresponding quantities of the black hole. Furthermore, we obtain stationary
solutions of the Navier-Stokes equations in four dimensions, which yield
predictions for (yet to be constructed) charged rotating black strings in AdS_5
carrying nonvanishing momentum along the string. Finally, we consider
Scherk-Schwarz reduced AdS gravity on a circle. In this theory, large black
holes and black strings are dual to lumps of deconfined plasma of the
associated CFT. We analyze the effects that a magnetic field introduces in the
Rayleigh-Plateau instability of a plasma tube, which is holographically dual to
the Gregory-Laflamme instability of a magnetically charged black string.
