ABSTRACT: Laser-cooling and trapping methodologies have opened a myriad of new frontiers which are extending our understanding inside and outside the realm of traditional atomic physics. Cold Rydberg gases and plasmas, which are generated by laser-exciting cold atom clouds near or above the ionization threshold, have displayed a variety of scattering mechanisms which lead to novel system dynamics at low magnetic field. Extending these studies to strong magnetic fields holds great promise, including the potential of achieving a strongly-coupled two-component plasma and observing exotic atomic drift orbits which resemble microscopic Penning traps. For these reasons and others we have developed a superconducting atom and plasma trap with a bias magnetic field of three Tesla, almost 20x larger than previously achieved. I will describe the basics of our laser-cooling and trapping techniques and the design and functioning of our superconducting atom and plasma trap. I will also discuss the dynamics observed in cold Rydberg gases and plasmas at low-magnetic field and show some of our early results at strong magnetic fields.