  The large magnetic fields of neutron stars and produced in heavy-ion
collisions motivate investigation into the response of strongly-interacting
matter to extreme magnetic forces beyond just theoretical interest.
Furthermore, the varying temperature $T$, baryon chemical potential $\mu_B$,
and aforementioned magnetic fields $B$, of these systems leads to questions
concerning the phase structure of Quantum Chromodynamics (QCD) at large. At low
temperatures, superconducting phases become a possible candidate for the ground
state in the $\mu_B$-$B$ plane. This thesis investigates two scenarios where
these phases emerge at $T=0$, with an emphasis on the type-II regime.
  Preceding the presentation of these works, the $\mu_B$-$B$ plane of the QCD
phase diagram is reviewed such that the results can be placed in the wider
context of this plane.
