Louis Neel's theories of thermoremanent magnetization (TRM) underlie all of rock magnetism. Neel's relaxation time equation for thermal activation of single-domain (SD) moments has been verified over geological time and temperature scales by laboratory thermal demagnetization of TRM overprints acquired in nature. For multidomain (MD) grains, disagreement with Neel's predictions is explained by re-equilibration of domain walls by the changing internal demagnetizing field during heating. Much effort has been devoted to testing the laws of additivity, reciprocity, and independence of partial TRMs, which partition the blocking temperature range and appear in nature as successive overprints of the original TRM. For SD grains, the laws are explained by Neel's theories and are verified experimentally. For MD grains, additivity holds but partial TRMs do not demagnetize over exactly the original blocking temperature interval (nonreciprocity) and are not entirely independent of one another when acquired in different directions. The current frontier in rock magnetism is to overcome this nonideal partial TRM behavior in order to extract precise and trustworthy records of ancient Earth's magnetic field directions and intensities.