Superconducting phases of strongly-interacting matter in large magnetic fields

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.