Laser cooling and magnetic trapping of (85)Rb atoms have been performed in extremely strong and tunable magnetic fields, extending these techniques to a new regime and setting the stage for a variety of cold atom and plasma experiments. Using a superconducting Ioffe-Pritchard trap and an optical molasses, 2.4 x 10(7) atoms were laser cooled to the Doppler limit and magnetically trapped at bias fields up to 2.9 T. At magnetic fields up to 6 T, 3 x 10(6) cold atoms were laser cooled in a pulsed loading scheme. These bias fields are well beyond an order of magnitude larger than those in previous experiments. Loading rates, molasses lifetimes, magnetic-trapping times, and temperatures were measured using photoionization and electron detection.