  We investigate the phase diagram of QCD-like gauge theories at strong
coupling at finite magnetic field $B$, temperature $T$ and baryon chemical
potential $\mu$ using the improved holographic QCD model including the full
backreaction of the quarks in the plasma. In addition to the phase diagram we
study the behavior of the quark condensate as a function of $T$, $B$ and $\mu$
and discuss the fate of (inverse) magnetic catalysis at finite $\mu$. In
particular we observe that inverse magnetic catalysis exists only for small
values of the baryon chemical potential. The speed of sound in this holographic
quark-gluon plasma exhibits interesting dependence on the thermodynamic
parameters.
