Recent advances in magnetic field generation have made experimentally accessible new regimes in magnetized high energy density physics. However, relatively little is currently known about the effects of kilotesla-level magnetic fields in relativistic laser-produced plasma. In this dissertation, I discuss a number of common plasma configurations, including solid targets and laser propagation in underdense plasma, in which applied magnetic fields can fundamentally alter plasma dynamics and impact important observables, such as ion and electron energy. In this regime, the changes induced by the magnetic field proceed mostly from the magnetization of hot electrons. Crucially, clear effects can be produced even when the magnetic field is not initially strong enough to magnetize electrons, suggesting that experimentally available applied magnetic fields may now be capable of delivering improvements for applications of relativistic short pulse laser-plasma interaction.