A simple and elegant interpretation of thermoremanent magnetization (TRM) in uniformly magnetized single-domain (SD) grains was given by N¿el 50 years ago, but the TRM acquisition processes in larger, nonuniformly magnetized grains are more varied and difficult to describe theoretically. SD TRM is a frozen high-temperature partition between two microstates: spins parallel or antiparallel to an applied magnetic field. Nonuniformly magnetized grains have a much greater choice of microstates (local energy minimum or LEM states), and partitioning among various LEM states continues to change during cooling. These changes may involve Barkhausen jumps of domain walls between positions of minimum local energy or nucleation of new domains and walls. Because of the lower remanence capacity of nonuniform microstates compared to the uniform SD state, TRM intensity decreases as grain size increases, although certain microstates, e.g., single-vortex states, seem to contribute little to TRM. Thermal demagnetization of TRM begins just above room temperature and continues to the Curie point, quite unlike the sharp unblocking of SD TRM. This continuous demagnetization, resulting from changes in microstates driven by the changing internal demagnetizing field during heating, profoundly affects the separation of different components of natural remanent magnetization and the determination of paleomagnetic field intensity. ¿ 1998 American Geophysical Union