Electrohydrodynamically driven active particles based on Quincke rotation have quickly become an important model system for emergent collective behavior in nonequilibrium colloidal systems. Like most active particles, Quincke rollers are intrinsically nonmagnetic, preventing the use of magnetic fields to control their complex dynamics on the fly. Here, we report on magnetic Quincke rollers based on silica particles doped with superparamagnetic iron oxide nanoparticles. We show that their magnetic nature enables the application of both externally controllable forces and torques at high spatial and temporal precision, leading to several versatile control mechanisms for their single-particle dynamics and collective states. These include tunable interparticle interactions, potential energy landscapes, and advanced programmable and teleoperated behaviors, allowing us to discover and probe active chaining, anisotropic active sedimentation-diffusion equilibria, and collective states in various geometries and dimensionalities.