In a hot toroidal plasma produced in the laboratory magnetic instabilities arise spontaneously and alter the large-scale structure of the plasma. Many of the processes that accompany this self-organization have counterparts in astrophysics. The toroidal plasma rotates and rapidly transports angular momentum in the radial direction, reminiscent of momentum transport in accretion disks. Plasma current is generated spontaneously producing a flux-conversion dynamo, possibly similar that that which might occur in astrophysical jets. Ions are heated during self-organization, similar to that observed in the solar wind. Magnetic field lines become chaotic, leading to energy transport as posited to occur in cooling flows in galaxy clusters. Mechanisms underlying all these laboratory processes are understood through detailed experiment and comparison to theory.